DATA BASE ACCURACY AND INTEGRITY AS A PRECONDITION …

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DATA BASE ACCURACY AND INTEGRITY AS A

PRECONDITION FOR OVERHEAD ALLOCATIONS

Harry H E Fechner

Doctor of Philosophy

The University of Western Sydney

Sydney, Australia

2004

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Certification

This is to certify that to the best of my knowledge, the research presented in this

dissertation is my own and original work, except where relevant sections and

references are duly acknowledged. This dissertation has not been submitted

previously in its entirety or substantial parts of it for a higher degree qualification

at any other university or higher educational institution.

Harry H E Fechner

28 January 2004

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Acknowledgements

There are numerous individuals that deserve special acknowledgment for their

assistance and contribution during the period of my candidature and to them I

express my sincere appreciation. Special thanks must go to my supervisor Assoc.

Prof. Rakesh Agrawal from the University of Western Sydney and co-supervisor

Prof. Graeme Harrison of Macquarie University. I am extremely grateful for the

patience and expert guidance I received from Prof. Agrawal during our many

thought-provoking discussions.

I am also grateful to a number of individuals who provided feedback and

commentary on aspects and content issues of my thesis during presentations at

international accounting conferences. While the list of these individuals is too

numerous, I would like to acknowledge the lengthy discussions I had at various

times with Prof. Malcolm Smith from the University of South Australia, Prof Clive

Emmanuel from Glasgow University, UK, Dr Michael Tayles of Bradford

University, UK, Prof Marc Massoud of Claremont College, California, USA, Prof.

Cecilie Raiborn of Layola University, Louisiana, USA, Prof. Rashid Abdel Khalik,

University of Illinois, USA, Prof Ted Davies, Aston University, UK and Prof Rob

Chenhall of Monash University, Melbourne Australia.

Additional thanks must go to the participants at the various sessions at many

international accounting conferences that provided -through questions and

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feedback- many thought provoking additional research investigations to include

in the final dissertation.

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Table of Contents

Certification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1. The Study Relevance to the Discipline . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.2 Contribution of Research to the Discipline . . . . . . . . . . . . . . . . . . . . 29

1.3 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

1.4. Research Methodology and Methods . . . . . . . . . . . . . . . . . . . . . . . . 33

1.4.1 Mathematical Techniques employed for model development. . 35

1.5 Structure of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

1.6 Definitions, Key Assumptions and Limitations. . . . . . . . . . . . . . . . . . 40

Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Key Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2. Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.1.1. Traditional Organisational and Operational Environments . 48

2.2.2 The Full Cost (or Absorption Cost) Concept. . . . . . . . . . . . . . 51

2.2.3 The Variable Cost (or Direct Cost) Concept. . . . . . . . . . . . . . 59

2.2.4 Standard Cost Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.2 The Changing Organisational and Operational Environments. . . . . . 63

2.2.1 Activity-Based Costing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.2.2 The Theory of Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 74

2.2.3 Strategic Management Accounting . . . . . . . . . . . . . . . . . . . . . 79

2.2.3.1 Critical Evaluation of Emerging

Management Accounting Systems . . . . . . . . . . 83

2.2.3.2C Case Study Based Comparison between

ABC and MAS. . . . . . . . . . . . . . . . . . . . . . . . . . 83

2.2.3.3 Error Incidence and System Accuracy . . . . . . . 92

2.2.3.4 The (IR)Relevance of Cost Management

Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

2.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

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3. Model Development. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

3.1.1. Database Integrity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

3.2 Development of a Pareto Frontier Model. . . . . . . . . . . . . . . . . . . 125

3.3 Data Base Generation and Pattern Recognition . . . . . . . . . . . . . . . 132

3.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

4. Case Study Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

4.2 Case Study Analysis Stock Exchange Data. . . . . . . . . . . . . . . . . 154

4.2 Case Study Analysis University Enrolment Data . . . . . . . . . . . . . . 156

4.3 Case Study Analysis Inventory Data . . . . . . . . . . . . . . . . . . . . . . . . 166

4.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

5. Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

6. Summary and Future Research Suggestions . . . . . . . . . . . . . . . . . . . . 185

6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

6.2 Major Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

6.3 Future Research Suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

List of Publications by Author relating to Thesis . . . . . . . . . . . . . . . . . . . . . . 202

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List of Tables

TABLE 2-1 A summary of surveys: elements of cost . . . . . . . . . . . . . . . . . . . . . . . . . . 50

TABLE 2-2 [Period 1](Product unit data) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53



TABLE 2-5 Comparison between MAS and ABC overhead allocations . . . . . . . . . . . . 89

TABLE 2-6 Regression result of Total Overhead on Direct Labour Costs . . . . . . . . . . 91

TABLE 2-7 Error incidence in [abc] product costing approach . . . . . . . . . . . . . . . . . . . 94

TABLE 2-8 (Product data taken from Pattinson and Arendt (1994:61)) . . . . . . . . . . . 100

TABLE 2-9, Product data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

TABLE 2-9a Product cost and contribution margin data . . . . . . . . . . . . . . . . . . . . . . . 106

TABLE 2-9b Cost Pool data using different cost drivers . . . . . . . . . . . . . . . . . . . . . . . 107

TABLE 2-10 Example (Set-up cost pool) of individual product activity cost calculations 108

TABLE 2- 11 Constraint Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

TABLE 2- 12 Results report of LP analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

TABLE 2-13 Profitability under varying product mix selections . . . . . . . . . . . . . . . . . 113

TABLE 2-14 Opportunity costs under different product mix constraints. . . . . . . . . . . . 114

TABLE 3-1 Results of ANOVA for data distribution of 8 (500 items) data bases . . . 135

TABLE 3-2 Results of ANOVA for data distribution of 8 (1000 items) data bases . . 136

TABLE 3-3 Results of ANOVA for data distribution of 8 (2500 items) data bases . . . 137

TABLE 3-4 Results of ANOVA for data distribution of 8 (4000 items) data bases . . 138

TABLE 3-5 Error data for Incremental and Point Differences . . . . . . . . . . . . . . . . . . . . . .141

TABLE 3-6 Results of ANOVA for data distribution of 5 random selected data

bases from the 500, 1000, 2500 and 4000 items data bases

with varied parameters for price, demand and shape factor. . . . . . . . . . . 149

TABLE 4-1, Results of ANOVA for Australian Share data("=.05) . . . . . . . . . . . . . . . . 155

TABLE 4-1a F-test for daily transactions/model values("=.05) . . . . . . . . . . . . . . . . . . 155

TABLE 4-3 (University 13) Results of ANOVA for 5 year DEST data ("=.05) . . . . . . 158

TABLE 4-4 (University 13) F-test for yearly enrolment records/model values (("=.05) 158

TABLE 4-5 ANOVA for each of the 12 universities’ 5 year students enrolment records160




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TABLE 4-18 Results of ANOVA for Inventory data("=.05). . . . . . . . . .. . . . . . . . . . . . . . . . .167

TABLE 4-18a F-test for Model/Inventory("=.05) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

TABLE 4-19 Model parameters for Case study data . . . . . . . . . . . . . . . . . . . . . . . . . . 169

TABLE 4-20 Cost Allocation Variances (Actual v Confidence Limits) . . . . . . . . . . . . 171

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List of Figures

FIGURE 1-1 Fechner’s Strategic Management Accounting Framework . . . . . . . . . . . . . 27

FIGURE 1-2 Framework for Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

FIGURE 2-1 Percentage changes of Material, Labour and Overhead costs over

3 periods for Product A, Products B, C and D show similar trends basis. 56

FIGURE 2-2, Percentage changes of Material, Labour and Overhead costs over

3 periods for Product A as proportion of the selling price; Products B, C

and D show similar trends basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

FIGURE 2-3 (Fig. 1-1 repeated here for clarity) Strategic Management Accounting

Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

FIGURE 2-4 Pareto Frontier, sorted by Direct Labour Hours . . . . . . . . . . . . . . . . . . . . . 85

FIGURE 2-5 Product over/under overhead distribution for the JDCW data . . . . . . . . . . 87

FIGURE 2-6 ABC compared to Traditional MAS Product Cost Portfolio . . . . . . . . . . . 101

FIGURE 2-7 Activity Cost Variation [Benchmark - ABC] . . . . . . . . . . . . . . . . . . . . . . . 110

FIGURE 3-1 Data Base and Model Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

FIGURE 3-2 Typical Incremental Error Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

FIGURE 3-3 Error Distribution of Point Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

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Abstract

Interest in more accurate assignment of overhead costs to establish credible

product/service cost profiles has assumed substantial prominence in much of the

recent debates on management accounting practices. While the promotion of

“new” cost management systems and in particular Activity Based Costing [ABC]

has promised to address many of the perceived shortcomings of more traditional

and long established techniques, the lack of its implementation success raises

some concern as to the validity and value of these “new” system designs.

Survey evidence from a number of different sources involving the evaluation of

past and current practices seem to identify the continued usage and application

of traditional cost management techniques and furthermore support a preference

by management to rely on simplistic allocation models for overhead cost

assignments. An often criticised limitation of the traditional absorption cost

system, the most popular in the survey findings, has been its reliance on a single

volume based cost driver (mostly Direct Labour Hours, DLH) for allocating

overhead costs. As organizations increasingly have employed advanced

technologies in many of their operational domains, DLH may no longer represent

a sound proxy for these allocations.

A major purpose of this thesis is the development of a mathematical model that

is capable of computing overhead allocations on the basis of organisational

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specific dimensions other than DLH. While almost all data bases suffer from data

entry and omission errors, the information content contained in the data bases

often forms the basis for management decisions without first confirming the

accuracy of the data base content. The model has been successfully applied and

tested to detect internal consistency and data element detail accuracy. A total of

3200 random number generated data bases with varying number of elements as

well as characteristics that typify general inventory data base records were tested

and statistically evaluated to confirm the validity of the model. It was found to be

robust under all the subjected varying parameters and therefore able to detect

domain consistencies and data element inconsistencies.

Future research may test the applicability of the model with more diverse data

bases to confirm its generalisability as an investigative as well as predictive

model.

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Executive Summary

This thesis has developed a mathematical model that mirrors the general pareto

or unbalanced distribution of data base elements given pre-specified element

parameters. To test the model’s robustness, standard statistical analysis (ANOVA

and F-test) of comparing paired elements between random number generated

data and model computed data, as well as incremental data comparisons

revealed non significant outcomes, thereby confirming the validity of the model to

detect data base inconsistencies.

Data mining of existing data bases revealed pattern consistency over a number

of periods that allowed the application of the model to detect data base integrity

or domain consistency (data belonging to the same organisation over a number

of periods) and data element accuracy (empirical evidence identified the

existence of data element errors through inaccurate entry or omissions) by

comparing the existing data base elements with the model generated data.

A further contribution of the thesis is the application of the model to identify data

base errors in an organisation’s inventory and production records and applying the

model’s generated values for the allocation of overhead costs. This concept of

overhead allocations parallels the simplicity of the traditional absorption technique

but increases the accuracy of the allocation method. This application is not limited

to manufacturing organisations but can be equally well applied to service

organisations.

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Overhead allocations have consistently been criticised as arbitrary, incorrigible

and misleading in determining accurate product costs. Literature evidence, both

article and textbook based, often presents examples in which the overhead cost

component exceeds 45% of total product costs. Under these circumstances, any

different method (new?) of overhead allocations (assignment, distribution)

produces convincing results for consideration of such new methods, e.g ABC

costing methods. Surprisingly, a number of recent surveys of manufacturing

industries in different countries found that the average proportion of both

manufacturing and non-manufacturing overheads combined is around 30% (Drury

and Tayles, 1994; Joyce and Blaney, 1990; Dean et at., 1991). At this level, the

perceived benefit from a "more accurate" cost assignment method is substantially

reduced, which might explain that reported survey results on the subject of

overhead allocations often find no significant modifications to existing

Management Accounting System [MAS] practices.

While the debate about alternative management accounting systems remains a

contemporary issue amongst academics and practitioners alike, the most popular

of the suggested alternatives, Activity Based Costing [ABC], has had only limited

success when compared with the continued application of traditional MAS

techniques (Shim and Sudit, 1995). Survey results on the adoption and

implementation of ABC indicate that, in countries like the US, UK, Canada,

Australia, Japan and some European countries, the acceptance/implementation

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rate varies between 6% and 12% across the industry spectrum (Cobb et al.,1993;

Cooper et al, 1988; Drury and Tayles, 1994; Dean et al., 1991; Fechner, 1995;

Armitage and Nicholson, 1993).

A persistent problem mentioned in the literature on ABC implementation is the

substantial cost involved in maintaining the system apart from the initial costs of

implementation. Other comments have questioned the benefits of more “accurate”

product costs as some of the overhead allocation problems remain and require

similar subjective judgmental allocations as experienced in traditional MAS

(Kaplan, 1994a).

Furthermore, anecdotal evidence and testimonials question the benefit of a

system replacement that is difficult to assess as to its final value. In addition the

initial operational analysis as to the totality of all value adding activities and the

determination of appropriate cost drivers presents many managements with

system complexities that are difficult to conceptualise as to the overall

improvements that can be achieved. This overwhelming complexity of the

activity/cost driver matrix and the extent of the organisation’s product range are

recurring comments throughout much of the related literature in identifying the

reluctance by management to implement an ABC system.

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The premise of any of the proposed “new” systems is that the organisation will

benefit from better decision support systems and thereby ultimately improve

profitability. Although this premise is defensible, its validation can only be

supported if the organisation’s current operations are well within its existing

resource capacities. To demonstrate this proposition, an example of capacity

(operational) constraints for a given product mix is submitted to optimisation

analysis (Theory of Constraints). This example tests the usefulness of a number

of alternative overhead cost allocation systems to provide evidence for the

indifference that any of these systems offer in determining an organisation’s

optimal profitability.

Most of the operational analyses that precede the evaluation and subsequent

implementation relies on an organisation’s existing data bases. However, there

also seems to be a reliance on data base integrity without the necessary

verification for such assumption. One of the discernible characteristics of almost

all data bases is their unbalanced distribution of element items when ranked on

the basis of two dimensions of interest.

Alfredo Pareto was the first scholar to recognise such relationships and since his

introduction of this phenomenon subsequent writings on the subject have referred

to it as the Pareto principle or the 80/20 rule. A well known application of the

80/20 rule within the accounting domain is the A-B-C classification employed in

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inventory control system design. Identifying products on the basis of their

individual value in relation to the total value of inventories provides a sound

approach for determining the resources to be expanded in controlling a major

asset in most organisations. An extension to this product classification as to the

individual product value within the total product portfolio would be to analyse if the

product cost profiles follow a similar distribution with particular emphasis on the

overhead proportion. While it is hypothesised that the resource consumption of

products parallels this of the inventory classification ranking, normal statistical

analysis is applied to support such conjecture.

Chapter 3 covers the major contribution of this thesis. The development of a

mathematical model to determine the exact 80/20 relationship (or any other

combination) on the basis of the total number of products. Such a computational

model provides the analyst (management accountant) with a tool to determine the

individual product contributions and thereby assists in establishing a hypothetical

benchmark for resource comparison. Although such a model is useful in

determining the hypothetical resource allocations, and therefore a benchmark, the

model does not, however, identify any existing inefficiencies in product or process

design. The model developed (as shown):

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where P = total number of products in portfolioxi = ith product rank within portfolioyi cum = cumulative percentage of ith product contributionc = constant for a given data base.(xi/P)d = term that determines the shape parametere = base of natural logarithm (2.718281)

is capable of identifying existing data base inaccuracies that indicate domain

consistency and data item inconsistencies, therefore providing a sound basis for

data element attribute predictions. As the interest of the thesis is in comparing the

usefulness of existing overhead allocations methods, the model will be applied in

computing overhead allocations based on its pair wise comparison with the actual

data of an organisation’s inventory and production records. The benefit provided

by such overhead allocation method, is its application simplicity as well as the

accepted - but criticised - absorption costing method.

In chapter 4, three specific data bases (case studies) have been selected for their

perceived data integrity and to test the robustness of the model against actual,

rather than random number generated, data bases. Statistical analysis establishes

the accuracy of data element attributes as well as identifying domain

consistencies. While the outcome of the analysis was hypothesised, the results

were still somewhat surprising.

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Stock Exchange daily transaction data should be audited prior to its release into

the public arena and therefore display a high level of data accuracy. The data

contained inaccuracies that were explained by the providers of the data records

as rounding applications of nonmarketable securities.

Australian university data of student enrolments on the other hand is often

presented unaudited to governmental funding authorities and thereby invites

suspicion as to the accuracy of the data recorded. Again data analysis revealed

both domain inconsistencies and data item inaccuracies.

The third case study is a current research study in which the organisation is

preparing to implement an ABC system that has been imposed by its European

based parent company. Many of the pre-requites of system change over were not

well understood by the operations personnel and the existing system has no

separate overhead classification but a rather inappropriate single conversion cost

distribution by cost centre. The application of the developed model identified

existing data base inaccuracies and provided operations management of the

organisation with evidence of data entry and omission errors for investigation and

correction where appropriate.

Chapter 5 discusses in detail the analysis of error terms from the 3200 random

number generated data bases its implications and application to the inventory and

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production data base. It further provides application specific statistical error term

calculations that are necessary for the computation of data element parameters.

The final chapter provides a summary and direction for future research in the area

of model extension and resource efficiency improvements.

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1. The Study Relevance to the Discipline

1.1 Introduction

Early research investigating the effect of technology on organisational

design suggested that organisational structure will experience modifications

with the implementation and use of technologies (Woodward, 1965;

Perrow, 1967; Thompson,1967; Duncan, 1972). However, to modify and

then maintain those structures, control systems have to be designed to

achieve these objectives. The realisation of the existence of organisational

design interdependencies lead to the development of contingency theory

(Gordon and Miller, 1975; Hayes, 1983; Waterhouse and Tiessen, 1978).

Organisational theorists embraced this new framework as it had the

promise of explaining a large number of organisational variables and their

interdependencies.

From the basis of the contingency model a number of diverse studies were

conducted to support the hypothesised relationships between selected

variables. Technology, as one of the organisational variables of interest in

explaining organisational design changes, became a credible explanation

for the operations structural changes and the need to match control system

design with the new operational environment (Daft and Mclntosh, 1978;

Merchant, 1984; Mclntosh and Daft, 1987). The latter aspect has created

a substantial body of research with divided opinions about the relevance of

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management accounting systems in these new Advanced Manufacturing

Technologies [AMT] production environments (Kaplan, 1983, 1986b;

Johnson and Kaplan, 1987). There is, however, an equally substantial body

of research that argues in favour of retaining the traditional management

accounting techniques in modified forms to match the organisation’s

information needs (Drucker, 1990).

Traditional management accounting practices have received increasing

attention from accounting academics who question the relevance of these

traditional practices in an environment of expanding advanced technology

based production. Kaplan (1983, 1984, 1986a,1988, Johnson and Kaplan,

1987) has become the most prominent and vociferous critique of the

management accounting irrelevance movement. His contention is largely

based on anecdotal and case study testimonials, suggesting that, with the

advent of large scale adaptation of Advanced Manufacturing Technologies

by manufacturing industries, the function of traditional Management

Accounting Systems [MAS] as a tool for planning and control is no longer

defensible. He attributes this diminished functional role of MAS to the lack

of perceived independence from the financial accounting function.

This argument has some credibility, especially if the origin and

development of many of the currently practiced management accounting

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techniques can historically be traced to the scientific management era. It

was in this environment that production engineers developed most of our

contemporary management accounting techniques (Kaplan, 1986a).

Therefore, it appears to be quite reasonable to again consult with

production engineers and planners to gain a better understanding of what

type of operational measurement requirements are needed in an AMT

environment. Management accountants thereby have some obligation to

become more familiar with production operations to develop appropriate

modifications to existing MAS.

The adoption and implementation of AMTs by organisations are driven by

the organisation's desire to gain or maintain a competi tive advantage

whereby consumer needs of constant high quality products or services at

competitive prices become the motivating objective. To meet this dual but

previously sought to be mutually exclusive criteria, firms have concentrated

on cost reductions often in the areas of direct and indirect labour costs. The

product cost profile of organisations who have implemented some form of

AMT should therefore indicate a shift in the components of the product cost

profile. Furthermore, recent surveys (Drury and Tayles, 1994; Joyce and

Blaney, 1990) have indicated that differences in product cost components

between various industry groups exist.

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Such differences may also be indicative of the treatment of product cost

determinations within different industries and provide some information on

the overhead allocation methods applied. Overhead allocations have

consistently been criticised as arbitrary, incorrigible (Thomas, 1975) and

misleading in determining accurate product costs. Surprisingly, a number

of recent surveys of manufacturing industries in different countries found

that the average proportion of both manufacturing and non-manufacturing

overheads combined is less than 30% (W hittle, 2000; Drury and Tayles,

1994; Joyce and Blaney, 1990, Dean et al., 1991). At this level, the

perceived benefits from a "more accurate" cost allocation method are

substantially reduced, which might explain that reported survey results on

the subject of overhead allocations often find no significant modifications

to existing MAS practices.

However, if the overhead component constitutes only some 30% of the total

product costs, given the evidence of recent surveys, the question arises at

what level of overhead proportion will the traditional allocation methods

become questionable and jeopardise the value of information that is

conveyed to management for product related decision making. Literature

evidence, both article and textbook based, often presents examples in

which the overhead cost component exceeds 45% of total product costs.

Under these circumstances a different method of overhead allocations

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produces convincing results for consideration of such new methods, e.g

ABC costing methods. Activity-based-cost [ABC] overhead allocations, a

method popularised by academics and consultants as an alternative to

traditionally based allocations methods, lacks the universality of application

as it depends largely on product diversity and product level overhead cost

pools (Cooper, 1988).

It is encouraging to note the recent change in management accounting

thought toward strategic cost management. This relatively new approach

to the traditional management accounting practices provides a desired

integrative framework for linking management accounting, operations

management and strategic management to create a cohesive group of

functional activities. W ithin this framework, technology is regarded as a

consequence of strategic choices and management accounting systems

are tools that aid in the implementation of those strategies (Govindarajan

and Shank, 1990).

Strategic management accounting [SMA], is a relatively new development

in understanding the relationships that dominate organisational design and

its maintenance mechanisms through the appropriate application of

internal control systems. It has been advanced as the natural progression

of earlier contingency theory prescriptions. While the underlying

24

assumptions of this approach are not new, the framework does however,

recognise the functional interrelationships of strategic management,

operations management and management accounting (Govindarajan and

Shank, 1990). It further identifies the relative importance of product life

cycle [PLC] analysis as a linking mechanism between strategic choice and

supporting management accounting system designs.

Much of the MAS irrelevance debate (Kaplan, 1983, 1986b, 1988; Johnson

and Kaplan, 1987) has been concentrating on the lack of modification to the

traditional management accounting practices in organisations after the

implementation of some form of an AMT. The main arguments are based

on the presumption that AMTs tend to reduce the direct labour content as

a proportion of total product costs and at the same time substantially

increase the proportion of manufacturing overheads. The allocations of the

presumed increased overheads on traditional based labour costs as well

as capacity volume related distributions are considered to provide

inaccurate cost data for product related decisions (make v buy, retain or

abandon, product mix, etc.) and it is argued that for these reasons they

have lost their relevance as a management decision support system.

As Kawada and Johnson (1993) point out the difference between the

”accuracy school” represented by ABC advocates and strategic

25

management accounting is the emphasis each of these “schools” attach to

organisational issues.

Whereas the accuracy movement stresses that the internal product cost

accuracy leads to improved profitability, the strategic movement stresses

that the analysis of the external environment mandates corrections and

adjustments to the internal control system structures and decision support

systems. Both movements, however, tend to agree that the traditional

financial based cost management system is no longer appropriate for either

task.

To provide a clearer example of the differences in the way of thinking these

schools represent can best be demonstrated by the product/services

related questions they address. The ABC school (internal focus)

emphasises improved profits through accurate product/service costing

while the strategists (external focus) are preoccupied with the question of

what products the company should produce.

The relevance of either emphasis may be revealed by the strategic stance

the company adopts with regard to cost leadership or product/service

differentiation. Therefore, accepting that both schools of thought have a

valuable contribution to make to the survival and growth of organisations

26

requires the development of techniques that combine the assessment of

product cost profile accuracy with the evaluation of product desirability and

viability. The literature in general has treated each of these emerging

issues as separate and distinct paradigms with specific contributions to the

overall functioning of organisations. However, there seems to be a

considerable commonality between these issues and represents an

opportunity to develop a linkage that offers a synergy between them.

In a contemporary survey (Shields and McEwen, 1996) it was found that the

successful implementation of ABC, amongst other factors, is dependent on

linking it to the “company’s competitive strategy regarding organizational

design, new product development, product mix and pricing and technology”

(p.18). However, while the authors offered a number of examples where

such a linkage would be beneficial, there was no suggestion as to the

concept or operational technique that would promote such

interdependence. A common thread that links all company objectives is the

realisation that available resources are limited and that these limitations

impose resource constraints that require efficient management.

To evaluate the effect resource constraints impose on the optimisation of

the organisation’s objectives, a number of operations management

techniques have been available for some time, most prominent amongst

them is the Theory of Constraints (ToC).

27

FIGURE 1-1

Fechner’s Strategic Management Accounting Framework

As the term suggests, [ToC] is based on the concept that the main objective

for efficient organisational functioning is to achieve resource optimisation

by attenuating the demand for a firm’s products/services with its flow of

production including administrative and other supporting functions.

However, most traditional and “new” management accounting systems do

not consider the optimisation of physical and resource capacities when

determining appropriate cost assignments to individual products.

The analysis of an organisation’s external environment to assess its

comparative advantage (to answer questions as to what products should

28

be produced) must be linked to the organisation’s capacity to produce these

products efficiently and within the expected cost boundaries. Figure 1-1

illustrates these interrelationships and how the consolidation of the

“accuracy” and “strategy” schools form the foundation of the strategic

management accounting discipline that leads to the determination of an

organisation’s product/service portfolio.

The determination of an organisation’s optimal product/service mix requires

the utilisation of optimality models. Most common amongst these are

Linear [LP] and Mixed Integer programming [MIP] applications. For a more

detailed discussion refer to Kee and Schmidt (2000). Although, the TOC is

sometimes criticised for relying on deterministic assumptions and thereby

reducing its value in predicting product mix compositions, stochastic

models are less appropriate as “production related activities are

deterministic in nature” (Kee and Schmidt 2000:5). The authors further

suggest that neither the ABC model nor the TOC model will be able to

compute an optimal product mix when both labour and overhead costs are

of a discretionary nature but that their general model (Mixed Integer

Programming, MIP) computes an optimal product mix.

This analysis provides an opportunity to discover that profit optimisation is

dependent on capacity utilisation and/or market demand constraints which

29

illustrate that cost accounting systems of whatever design will have no

influence on the profitability outcome of the organisation (refer to Table 2.9,

2.9a, and 2.9b). Such results may help to explain the continued popularity

of traditional cost accounting techniques and the reluctance by

managements’ to implement contemporary systems such as Activity-Based

Costing.

This generalisation, however, needs to be moderated as it is difficult to

apply optimality models organisation wide and maybe restricted to the

analysis of functional units within the corporate framework.

Rather then suggesting that cost management systems are irrelevant when

determining an organizations profitability, the difficulty in implementing

optimality analysis corporate wide, refocuses the emphasis on cost

accounting systems capable of assigning or allocating overhead costs to

individual products/services on a credible basis.

1.2 Contribution of Research to the Discipline

Survey results (Drury and Tayles, 1994; Joyce and Blaney, 1990; Dean et

al., 1991; Fechner, 1995; Whittle, 2000) as well as a historical review

(Boer, 1994) clearly indicate that overhead cost proportions within a

product’s cost profile have not substantially changed over time and

30

organisations continue to prefer simplistic overhead allocation methods.

Although some of the evidence suggests that traditional allocation models

produce some inequitable overhead allocations within the organisation’s

total product portfolio it appears to be more appropriate to develop an

overhead allocation method that incorporates the changing environmental

circumstances but maintains the simplicity of an overall overhead allocation

method.

A major problem that has not been addressed by previous research is the

accuracy and integrity of organisational data bases that form the basis for

cost accumulation and subsequent cost allocations. Incomplete or

inaccurate cost accumulation pools may contribute to the claimed cost

distortions that have been identified in comparative cost management

system examples and case studies.

To address the dual problems of data base integrity and more equitable

overhead cost allocations this thesis will adopt a data mining technique to

identify data patterns within random number generated data bases from

which a predictive model can be developed. This model will then be tested

for its robustness against publicly available stock exchange data,

Australian university student enrolment records and company data bases.

Statistical tests to evaluate the model parameters against the actual data

will be applied to confirm its predictive value in determining overhead cost

allocations.

31

1.3 Research Objectives

This thesis will:

- develop a robust model for the allocation of overheads that is

based on the historical data pattern of the company’s

inventory and production records.

- analyse and test the commonal ity of data base patterns to

confirm the empirical evidence as to the existence of the

Pareto distribution - or 80/20 rule - in a number data bases.

- develop a mathematical model that mirrors the data

distribution of Pareto ranked cumulative element

arrangements to test its robustness under varying parameters.

To test such robustness standard statistical analysis of paired

element comparisons (Anova and F-test) as well as error term

analysis for incremental values and point estimates will be

conducted.

- identify data base integrity and data accuracy (as empirical

evidence suggests that almost all data bases contain data

element errors through inaccurate entry and omissions) by

comparing the initial data base with the model generated data

base for pattern consistency.

While the model will have universal applicability its parameters need to be

determined on the data pattern history of the individual organisation. By

32

accepting that each data base will have its unique pattern, it is

hypothesised that the data pattern within a given domain (organisation) will

display pattern consistency while such consistency is not expected across

different domains even within the same industry grouping.

If such findings are revealed by the analysis then a further benefit from the

model would be its ability to detect pattern inconsistencies within a domain

as unexpected and alert appropriate management levels to the possibility

of data errors and inaccuracies.

Once the data base integrity of a domain has been established, the model

will be applied to compute individual product overhead cost allocations on

the basis of the ranked data base element distribution of pre-specified

product attributes. Such pre-specified product attributes could include

product demand, material consumption and resource consumption amongst

others.

33

1.4. Research Methodology and Methods

Most data bases display nonlinear relationships between any dual content

data items of interest. Steindl (1965:18) recognised this fact and stated that

“for a very long time, the Pareto law [ the 80/20 principle] has lumbered the

economic scene like an erratic block on the landscape; an empirical law

which nobody can explain.” While this observation in itself does not provide

any new insights into the existence of such phenomenon, it does, however,

provide an opportunity to quantify through mathematical modelling the

individual data item contribution to the distinctive shape of the cumulative

distribution curve.

The application of the Pareto principle relies on the availability of a data

base that constitutes the population of data items of interest. Ranking of

items on the basis of two dimensions of interest will produce a typical

Pareto distribution. The development of a model that can mirror the Pareto

frontier produced by the ranking of data items, will allow the application of

such a model as a prediction tool of the items of interest. The purpose of

this thesis is to use mathematical modelling techniques to develop such a

model and apply it in the prediction of overhead costs for a company’s

product portfolio.

34

The development of the model required the testing of the specified model

parameters against a substantial number of data bases to ensure that it has

the robustness required to become a credible prediction tool.

The initial database testing will use a substantial number of random number

generated data bases with different data item populations. These data

bases will contain typical product cost characteristics where each of the

cost components of material, direct labour and overhead allocations are

randomly varied. To accomplish this task, a standard spreadsheet

application (Quattro Pro in this case) will be employed which has the

desired random number generator function to establish the database

combinations. Although there is no relevant literature to provide guidance

as to the population size required for mathematical modelling, a reasonable

population size that mirrors average inventory holdings of manufacturing

organisations in the range from 500, 1000, 2500 and 4000 items would

appear to be adequate. For each of the populations 100 random number

generated data bases ( a total of 3200 populations) will be compared with

the developed model to establish a statistically adequate sample size. To

further improve on the robustness of the model, an error term (deviation

between model computed values and database values) of +/- 5% in the fat

tail region of the distribution is considered appropriate. This level is

suggested as an acceptable error term as most standard statistical tests of

significance are set at a 5% level for model prediction validity.

35

The model will be tested against each random generated data base to

calculate the error term of its parameters against the item values of the

data base. A paired comparison using single ANOVA statistics together

with a standard F test will be used to establish the validity of the model

parameters.

1.4.1 Mathematical techniques employed for the model development

For the development and application of the model a number of

mathematical techniques were used to establish data base pattern

consistency as well as the analytical evaluation of existing overhead

assignment techniques. To establish the existence of a generalised Pareto

distribution (GPD) as suggested by Koch (1998) existing data bases need

to be investigated for pattern similarities in a data mining approach.

Data mining in the context of this thesis refers to the investigation of

appropriate existing data bases (populations), given some pre-determined

parameters or element characteristics, to identify data element patterns that

confirm the general accepted but anecdotal evidence of the Pareto principal

or unbalanced distribution.

The Pareto principal or unbalanced distribution should not confused with

the theoretical Pareto optimality concept. Pareto optimality is achieved

36

when the distribution of goods/services falls on the contract curve in a

modeled Edgeworth-Box diagram and represents the condition of optimal

resource/commodity/welfare distribution. The exchange of goods/services

beyond a point on the contract curve leads one consumer to be worth of in

his (her) indifference towards a bundle of goods/services. Although the

concept can also be applied to the production possibility frontier

hypothesis, it is not the purpose of this thesis to deal with the economic

rationale of Pareto optimality but instead introduces the concept of Pareto

efficiency in which a vital few and not the trivial many affect the output

condition of the firm.

Pareto’s original discovery of the wealth distribution in a certain population

followed a 20/80 pattern (20% of the population enjoyed 80% of the

wealth). Further investigation by Pareto (Koch, 1998:6) revealed that this

unbalanced distribution was repeated consistently over different

populations and different time periods. This repetition of the same pattern

followed an almost mathematical precision. While the generalised Pareto

distribution has been mathematically formalised, it is mostly applied in the

analysis of fat or thin tail distributions.

While the unbalanced distribution clearly identifies the existence of non

linear relationships between variables of interest another form of data

37

element analysis and prediction is based on the assumption of linear

relationships between data element variables. Linear programming as well

as linear regression analysis assumes linear relationships amongst the

variables of interest. A number of overhead allocation techniques have

been based on the concept of linear behaviour of variables in predicting

future outcomes and cost assignments.

Linear programming (LP) on the other hand tends to establish a optimal

solution to a given set of constraints within a given and pre-specified

environment. Resource utilisation and capacity analysis are two of the most

popular applications of LP. A more contemporary application of LP can be

found in the Theory of Constraints (ToC). Here the presumption exists that

in any operating environment a bottleneck situation can be found and

through its initial elimination other bottleneck situations are revealed for

further analysis and elimination. This step approach will ultimately lead to

a optimal solution that ensures operational efficiency. As the ToC assumes

linearity relationships some of its analysis are open to criticism. The

assumption of labour resources, as a capacity variable, behave linear has

been shown to be inaccurate as the learning curve concept was empirically

validated. However, the concept of LP is relevant in comparing a number

of different overhead assignment techniques to determine if any of these

techniques are superior in predicting optimal profitabilty of an organisation.

38

By comparing the outcome of the LP computations of the different overhead

assignment techniques, sensitivity analysis in the form of shadow price

differences provides a useful analytical tool.

Sensitivity analysis is a concept that ensures the testing of computational

outcomes by evaluating the results of a number of input variable changes.

This concept is a pre-requisite for any model development to determine the

robustness of the model’s predictive and analytical ability. Sensitivity

analysis is mostly based on statistical evaluation of the computed value

within pre-defined error limits.

39

Use of Model

derived data

Thesis Contribution Existing Applications

Data Entry

Keyboard Entry

Barcode

Electronic Data Transfer

Develop mathematical

Model for testing Data Audit (Sample testing)

base accuracy

Evaluate existing Comparison of

allocation models Contemporary

using optimisation Allocation Models

techniques

Compare Results.

Statistically evaluate results

of available Databases and

compute model-based data

element properties.

Apply to Overhead Allocations.

FIGURE 1-2

Framework for Thesis Structure

Establish

Databases

Testing Database

Accuracy

Modeling of

Database

Prediction (Forecasting) Modeling

Transfer to other Databases

Overhead Allocation Models

Use of partially

corrected data

Application of

Data

40

1.5 Structure of Thesis

The thesis comprises six chapters that follow a traditional development of

literature review, formulation of a hypothesis or in the case of this thesis the

development of a mathematical model that will be tested against existing

data bases to validate its robustness. A comparative analysis between the

computed model values and the existing data bases will be conducted and

the results are reported in a separate chapter. Finally, a summary of the

comparative analysis and recommendations for future research

applications of the model is presented. Figure 1-2 depicts a graphical

presentation of the thesis structure.

1.6 Definitions, Key Assumptions and Limitations.

Definitions

There are a number of terms introduced throughout the thesis that require

explanation and clarification. The major part of the thesis is devoted to the

development and testing of a mathematical model that enables users to

detect data base domain consistency and data base integrity by comparing

computed model values forming a Pareto frontier with the Pareto frontier

generated by the existing data base. Once these conditions are confirmed,

the model can be applied to allocate organisational overheads to products

or services to establish a credible cost profile and serve as a prediction

model for budget considerations and preparation.

41

A data base domain in the context of this thesis refers to the data base

composition of share trading records, university records and organisational

inventory records over a number of periods were each period’s data base

element ranking remains statistically similar. While only three different data

base groups were selected for analysis, empirical evidence (Koch, 1998)

suggests that the Pareto distribution (80/20 rule) can be applied to almost

any data base collection.

Statistically similar implies that the F and P values display insignificance,

thereby supporting the contention of domain consistency over successive

periods. However, inventory records from different organisations, share

trading records from different stock exchanges and student enrolment

records from different universities will have different Pareto frontier

characteristics and therefore can be identified as not belonging to the

domain of interest. An example, two university enrolment data base records

would show statistical significance - coming from different domains - while

the enrolment data records from the same university over a number of

periods are expected to show no statistically significant differences. While

there is no theory for such propositions the mathematical modeling process

to generate random number (characteristic) data bases employed for the

testing of this proposition will provide the basis for the lack of existing

theory.

42

Data base integrity should be understood as the correctness and

completeness of data base elements that have been compiled by recording

transactions or similar events into a common data base designed for the

capture of element characteristics with information content that infers

attribute commonalities. Empirical evidence, although sparse, suggests that

most, if not all, data bases contain data entry and data omission errors and

thereby impinge on the data base integrity.

A Pareto frontier refers to the curvature that is formed when a data base is

ranked and sorted on two predetermined dimensions and the item

frequency distribution is arranged in a cumulative ascending sequence such

that x1 > x2 >x3 >.......xn. Although the Pareto principle has been accepted,

its validation has only been confirmed through practical applications of

element ranking and ordering.

43

Key Assumptions

A number of assumptions have been made in the development of the

model. Firstly, the assumption is made that all data bases follow an

unbalanced distribution (the Pareto principle) but there are no tools or

techniques that detect data base inaccuracies as the element arrangement

can only use the available data.

Secondly, any data base which involves the recording of events or

transactions that are compiled by operators with or without technical

support systems will contain data entry and omission errors. While other

sources of errors have been discussed in various literature, for the purpose

of this thesis, entry and omission errors are the most relevant components

of interest.

Thirdly, simplified overhead allocations are preferred by practitioners which

is supported by recent survey evidence on overhead assignment methods

and further reveal a lesser reliance of these methods in decision support

system applications by corporate managements.

Fourthly, the generation of random number generated data bases is a

better proxy of “real” data bases as these are free of both data entry and

data omission errors and, furthermore, allow the varying of data base

44

element characteristics at random as well as varying the Pareto frontier or

shape factor to mirror any “real” data base Pareto frontier.

Limitations

A number of limitations must be identified. The major limitation is the model

testing against random generated data bases as validation of its robustness

using a limited number of element characteristics. Furthermore, the use of

data base analysis on the basis of only two predetermined element

characteristics may limit the model’s application in more complex and

interdependent data base element relationships. This limitation may apply

to the model’s general applicability but it must be understood the purpose

of the model development was to provide an alternative overhead

allocation method. The most popular practiced techniques also rely on a

simple two-dimensional allocation, volume and demand. Overhead

allocations in general have been criticised as incorrigible and arbitrary and

as such, the model does not resolve this allocation problem. The model

does, however, redress the allocation problem associated with product

additions and deletions by the re-ranking process rather than the continued

application of a single volume denominator.

Another limitation that could be advanced is the need to analyse an existing

data base before any model application can become effective. While such

a precondition may have been a limitation in past periods where

45

computational resources were scarce and expensive, contemporary

inexpensive availability of extensive computer resources and software

applications are no longer a defensible restriction.

46

2. Literature Review

2.1 Introduction

The allocation problem has plagued accounting theory for many decades.

Accounting allocations are found in many areas ranging from financial

accounting standards of generally accepted accounting principles (GAAP)

to the internal or management accounting practices involving the allocation

of general overheads to products for purposes of inventory valuations and

managerial decision making concerning product mix and product viability

determinations.

Athur L, Thomas could be credited with being a most prominent opponent

of the allocation debate. In a 1975 article he suggested that any form of

accounting allocations are almost always incorrigible and therefore never

preferable to a refusal to allocate. He reaches this conclusion after careful

theoretical analysis and provides a number of examples that demonstrate

the limitation of any one allocation method over any other. He further

argues that the incorrigible nature of allocations makes it highly unlikely the

accounting profession will ever achieve a consensus on what can be

regarded as the “best” allocation scheme while there are alternative

schemes that compete for dominance. Thomas (1975) concludes that the

best alternative must therefore be, not to allocate.

47

While the theoretical arguments that underpin the non allocation position

proposed by Thomas are grounded in rational economic thought, these

concepts find limited acceptance in management accounting approaches

to determine product costs and thereby direct resource allocations, yet

another area of incorrigible allocations. Much of the recent debate

concerning the relevance or otherwise of traditional management

accounting is concerned with the perceived inappropriateness of overhead

allocation techniques. One of the most prominent proponents of the

irrelevance movement Robert S. Kaplan argues convincingly that the need

to allocate overhead costs on a single volume based cost driver is

inappropriate in a changed environment that is dominated by advanced

product and process technologies. His suggested alternative of Activity

Based Costing [ABC] has found some resonance in organisations, whi le

some of his critics claim that this technique is based on historical data and

relies also on subjective allocations for some of the identified overhead

classifications.

Another contemporary approach to modify traditional management

accounting techniques has been advanced by Eli Goldratt (Goldratt and

Cox, 1992) in promoting the need for organisational constraint recognition

and the subsequent effort to reduce or eliminate such constraints. Goldratt’s

Theory of Constraints [TOC] further suggests that any current management

48

accounting technique is stifling the application of TOC and has little

relevance in improving an organisation’s profitability. He defends this

proposition by claiming that the main purpose of any organisation is the

creation of wealth and that the generation of improved cash flows becomes

a consequence of improved process efficiencies.

Each of these theories does contribute to a better understanding of the

issues that have confronted the accounting profession for decades but

provides only limited application relevant to the practising accounting

profession. In the following sections a number of techniques for each of the

stated theories are discussed and the final section provides a critical

evaluation of the issues presented.

2.1.1. Traditional Organisational and Operational Environments

The need to determine the cost of individual products in an organisation’s

product mix is a basic information requirement for managerial decision

making. The development of fundamental techniques to produce accurate

product cost data goes back in history to the establishment of organisations

involved in the production of manufactured goods. As mechanisation of the

production process was limited to the prevailing technology most of the

production processes were reliant on manual labour skills. The conversion

process of materials to sellable products required a substantial amount of

49

direct labour effort and volume production was a function of labour capacity.

What was less determinable were the indirect costs of production as these

related to the productive output. Planning, control and monitoring functions

are an integral part of organisational life and incur a substantial cost. These

indirect costs have been referred to in various terms. Most common

amongst the terminology are overhead costs, manufacturing burden or

production on-costs. ‘Overhead costs’ seem to be the most commonly

referred to cost term of these genre and will be used throughout this thesis.

Accepting the early industrial setting of production capacity being a function

of labour skills availability, it was a common sense assumption to base the

distribution of overhead costs on the consumption of direct labour involved

in the production of manufactured goods. Such reasoned approach allowed

the allocation of overhead cost to individual products on the basis of direct

labour hours consumed in the production of these goods. As competitive

environments were of lesser consideration, the product’s final price was

determined by the total manufacturing costs (material, labour and

overhead) to which a percentage was added to recover other related

organisational costs (selling, administration, etc.) to ensure that a

satisfactory profit was attained.

50

TABLE 2-1,

A summary of surveys: elements of cost

Cost

elements

Whittle

(2000)

%

ACCA

(1993)

%

Murphy &

Braund

(1990)

(1985)

%

Kerreman

(1991)

%

Schwarzbach

(1985)

%

D.Mat 57 50 50 47 55 58

D.Labour 15 12 18 18 21 13

O/H Var.

Fixed

11

14

38* 32* 35* 24* 29*

Other 3

Total Costs 100 100 100 100 100 100

*Split between fixed and variable not reported in survey results

Source: Whittle, N., (July/August 2000), “Older and Wiser”, Management Accounting, p.35

W hittle (2000) has compiled an overview of a number of surveys that

investigated the ratio of product cost components over a 13-year period.

W hile such compilation cannot be regarded as definitive, it does,

nevertheless, provide a less biased review of changing product cost

elements.

What is noticeable in Table 2-1 over the review period is the rather

constant proportion of direct labour as a proportion of total product costs.

A similar review (Boer, 1994) covering an extended period from 1850 to

1987 supports this trend by claiming that differences in labour percentages

across industries have existed for many years but trends within industries

51

have experienced little change. As most of the surveys cover a broad

sample of industries, the data refers to averages, therefore allowing for

industries to be either substantially above or below these percentages.

Another aspect of the accuracy debate is the analysis of existing processes

and activities and a subsequent regrouping of these activities into

homogeneous cost pools. Such analysis is limited as it does not investigate

the current process inefficiencies or resource constraints to recommend

optimisation strategies. A useful starting point in any operational analysis

is the identification of capacity and resource constraints. Capacity

constraints can be limited to the physical means of production whereas

resource constraints should include availability of human resources and

supply chain limitations.

2.1.2 The Full Cost (or Absorption Cost) Concept.

The full cost concept (or absorption cost concept) was therefore an

acceptable method for product pricing purposes and managerial decision

making with regard to product mix considerations and (dis)continuation of

individual product manufacture. Another often cited advantage of the full

cost concept is the risk reduction in managerial pricing decisions as the full

cost constitutes the fundamental part of the pricing equation. One of the

drawbacks, however, is related to efficiencies. Should the labour skill levels

52

differ amongst a number of operatives in producing a given unit, the total

direct labour hours vary resulting in different overhead applications for the

same unit of production. Such potential inconsistencies were overcome by

establishing production standards as benchmark for comparison and led to

the development of standard costing practices. It was not uncommon in the

earlier part of the industrial revolution to have a labour cost content in

excess of 50% with materials contributing another 30% to 40% and the

reminder of the total product cost being the allocated overhead.

An example will demonstrate the initial product cost profile and through the

development of labour reducing production processes the change in the

main cost components (material, direct labour and allocated overhead

costs). The example is based on a number of premises that establish the

parameters of the computational results.

Firstly, a product that has remained fairly consistent in appearance,

functionality and consumer demand over a longer temporal dimension has

to be identified (eg. Kellogs Corn Flakes, Coca Cola, Household Furniture

to name a few). For simplicity the products are referred to as A, B, C, D.

Next the operating capacities have to be established. The annual

production capacity is based on 100,000 direct labour hours [DLH] with a

53

total overhead cost of $800,000. Each unit of product consumes a standard

number of labour hours and thereby determines the output level of the

organisation. Material costs and the number of hours per unit are given in

Table 2-2. As the total overhead costs are given as $800,000 and overhead

costs are recovered on the basis of direct labour hour capacity the

overhead application rate is $8.00/DLH ($800.000/100,000 DLH).

TABLE 2-2 - [Period 1]

(Product unit data)

Product

Number of units produced

A

10,000

B

10,000

C

10,000

D

10,000

Total

40,000

Material $35.00 $75.00 $30.00 $24.00

DLH

@ $10.00/h

2.00 4.00 3.00 1.00 100000

$20.00 $40.00 $30.00 $10.00

Overhead Allocation

@ $8.00/DLH$16.00 $32.00 $24.00 $8.00

Total Full Cost $71.00 $147.00 $84.00 $42.00

Profit Percentage (50%) $35.50 $73.50 $42.00 $21.00

Selling Price $106.50 $220.50 $126.00 $63.00

Gross Profit $1,065,000 $2,205,000 $1,260,000 $630,000 $5,160,000

With improved efficiencies attributable to advanced technologies the total

labour effort per unit of production is reduced by an average of 50% while

the total overhead cost increases by 100% which accounts for both

depreciation charges and technical skil l acquisitions. The changed

parameters are now ($1,600,000/100,000 DLH) a $16.00 overhead

application rate and a doubling of productive capacity. Table 2-3 reflects

these changes.

54


(Product unit data)

Product

Number of units

produced

A

20,000

B

20,000

C

20,000

D

20,000

Total

80,000

Material $35.00 $75.00 $30.00 $24.00

DLH

@ $10.00/h

1.00 2.00 1.50 0.50 100000

$10.00 $20.00 $15.00 $5.00

Overhead Allocation

@ $16.00/DLH$16.00 $32.00 $24.00 $8.00

Total Full Cost $61.00 $127.00 $69.00 $37.00


Selling Price $91.50 $190.50 $103.50 $55.50

Gross Profit $1,830,000 $3,810,000 $2,070,000 $1,110,000 $8,820,000

Assuming similar changes for a third period would produce an overhead

application rate of $32.00 ($3,200,000/100,000 DLH). In addition it is

assumed that the cost of materials remains unchanged due to component

reduction and less expensive alternative material supplies. Labour rates

have also been kept constant on the assumption that technology

replacement reduced the labour skills requirements and therefore would

reduce the cost of labour as well as the time required to produce a unit of

production. Table 2-4 reflects these additional changes.

55


(Product unit data)

Product

Number of units

produced

A

40,000

B

40,000

C

40,000

D

40,000

Total

160,000

Material $35.00 $75.00 $30.00 $24.00

DLH

@ $10.00/hG92

0.50 1.00 0.75 0.25 100000

$5.00 $10.00 $7.50 $2.50

Overhead Allocation

@ $32.00/DLH$16.00 $32.00 $24.00 $8.00

Total Full Cost $56.00 $117.00 $61.50 $34.50


Selling Price $84.00 $175.50 $92.25 $51.75

Gross Profit $3,360,000 $7,020,000 $3,690,000 $2,070,000 $16,140,000

The above example, although simplistic, clearly demonstrates the effect of

process improvements on the product cost profiles using the full cost

concept. The percentages created by assumption relate closely to survey

results of a study conducted across three industries (Banker et al., 1995).

While the arguments advanced by opponents of the traditional overhead

allocation technique have some relevance, the often criticised misallocation

of overheads on the basis of a single cost driver (DLH in the example)

seems to be exaggerated. An investigation by Boer (1994) supports this

contention by revealing that cost profile changes over the past 140 years

have not experienced the often projected dramatic changes suggested by

contemporary critics of traditional management accounting techniques. A

56

1990 Australian survey of manufacturing organisations across 13 different

industry groups revealed that the average product cost profile follows a

55%-20%-25% (material - labour - overhead) profile but varies substantially

across industries captured by the survey.

FIGURE 2-1, Percentage changes of Material, Labour and Overhead costs over 3 periods for

Product A, Products B, C and D show similar trends basis.

57

FIGURE 2-2, Percentage changes of Material, Labour and Overhead costs over 3 periods for

Product A as proportion of the selling price; Products B, C and D show similar trends basis

The example provided in Tables 2-2, 2-3 and 2-4 and illustrated in Figures

2-1 and 2-2 reflects the general status of these findings and confirms the

need to control and allocate overhead costs on a more computational

basis. The more dramatic cost profile change appears to be in the direct

labour and material groupings. As mentioned before both of these

categories have been held constant in relative cost terms over the three

periods but would produce a more dramatic change if these groups

experience increases over the review period. Overhead costs, however,

who had the most significant cost increases during the review period have

only experienced a moderate proportional cost increase. No attempt has

58

been made to identify different activities of the total overhead costs nor to

categorise overhead cost on the basis of cost behaviour into fixed and

variable components.

The benefits derived from such effort would have only a limited impact on

the selling price of the product. In the example, if we calculate the cost

groups as percentages of the selling price then the overhead proportion

reduces to 15.02%, 17.49% and 19.05% for each of the three periods as

illustrated in Figure 2-2. Even if it is possible to identify activities that can

be directly associated with the manufacture of a given product it is unlikely

that this will exceed 50% of the total overhead costs thereby leaving the

remaining 50% again to be allocated on a questionable basis.

Surveys by Anthony and Govindarajan (1983) found that 83% of

organisations use the full cost concept for product pricing of which 50%

used only manufacturing costs, and by Shim and Sudit (1995) found that

70% use full cost pricing, again 50% of those firms that responded relied

on manufacturing costs only for their pricing decisions. This survey

evidence clearly demonstrates the continued reliance on full costs by

organisations in determining their product prices. In the latter survey a third

category (this was not included in the initial survey by Anthony and

Govindarajan (1983) of market-based pricing revealed a 18% application

by responding firms. It can only be conjectured that, if the initial survey had

59

included the market based pricing strategy, the percentage distributions

between full cost pricing, variable cost pricing and market-based pricing

may have revealed a lesser trend reduction in the first two pricing

strategies.

2.1.3 The Variable Cost (or Direct Cost) Concept.

Whereas the full cost concept is based on organisational functions to

distinguish product costs and other organisational expenses, the variable

cost concept distinguishes these cost groups on the basis of cost behaviour

related to the production process. The main classification required to

determine product costs are the identification of variable and fixed cost

groups and assess which specific costs are related to the manufacture and

distribution of goods. As in any of the traditional or emerging cost concepts

there is little disagreement as to the material and direct labour cost

assignments, the arguments relating to achieve improved product cost

accuracy are concerned with the identification and assignment of overhead

costs.

The variable cost concept treats materials and direct labour identical to any

other concept but distinguishes the composition of total overhead costs.

Cost behaviour assumptions are not easily determinable and at times rely

on the experiences of operating personnel rather than verifiable

60

computational data. Fixed overhead costs (e.g. Depreciation, rental,

property taxes, etc.) are not included as product costs but become part of

other operating expenses such as administrative, selling and marketing.

Variable overhead rates which include such cost groups as setup costs,

material handling and quality control are treated as product costs and form

part of the product cost profile. The main difference to any of the data in

Tables 2-2, 2-3 and 2-4 would be changes in the amount of overhead costs

assigned to products. The full cost concept includes all overhead costs in

determining a product’s total cost. The variable cost concept, by only

including the variable overhead cost, will by logic, show a reduced total

product cost with similar trends amongst the cost groups over the three

periods.

In the early 1950s variable costing was popularised and embraced by

management as a better decision tool for product mix decisions because

it provided more accurate product costs based on trend analysis rather than

capacity volume predictions. Most arguments that are advanced against

the usefulness of absorption costing criticise the application of a single cost

driver as the determinant of computing a single overhead application rate.

Variable costing approaches often identify a number of cost pools (or

service departments) and associate appropriate cost drivers with these

cost pools to determine a number of process based overhead application

rates. The same principles can also be applied to the full cost concept.

61

Advantages attributed to the use of variable costs through the distinction

of fixed and variable costs are the ability to compute Cost-Volume-Profit

[CVP] data essential for planning and control management. Other

advantages relate to product cost decisions especially as these are related

to Make versus Buy and special order acceptance. However, the

arguments for or against one of these cost concepts reduces to

insignificance when a period’s production is sold without any inventory

accumulation. As many industries base their production environments on

a continuous improvement philosophy the progress towards zero

inventories is a feasible and likely scenario that would further reduce the

distinction being promoted between full costs and variable costs to a case

of irrelevance. Process improvements, however, will have to be reflected

in product data by providing production reports that present benchmark

levels for performance comparison.

2.1.4 Standard Cost Concept

Each of the two concepts previously discussed rely on past data to identify

the total cost of production and product unit cost profiles. Standard costs

provide a planning foundation that is no longer incorporating production

inefficiencies from past performances but computes product costs based

on current process technologies and labour skills. In additional advantage

derived from the use of standard costing is its ability to provide a base for

62

comparison at different levels of capacity utilisation. While the full cost and

variable costing concepts are useful in determining product costs for

inventory and pricing values, the standard cost concept is applicable to the

evaluation of operational efficiencies and resource consumption. It is based

on the premise that a given resource input must provide a determinable

production output and substantial deviations from this relationship instigate

formal investigations to correct undesirable situations.

The standard cost concept further supports much of the traditional

managerial philosophy of exception reporting. Other advantages that are

attributed to the concept of standard costs are improved cash and inventory

planning, the ability to support responsibility accounting-based

performance evaluation, improved unit cost profiles and incentive schemes

that are tied to predetermined resource consumption. Some disadvantages

have also been identified and include: the interpretation of variances and

the decision rule that initiates process intervention, performance evaluation

tied to incentive schemes are open to manipulation by affected operating

personnel and the concentration of supervisory personnel to minimise

variances may not lead to efficient operational processes as isolated

production sequences are reviewed.

63

Survey results by Gaumnitz and Kollaritsch (1991) and Cohen and

Paquette (1991) indicate a trend in the application of standard costs to

smaller units (departments) regardless of the organisation’s size nor its

industry membership. These results could be interpreted as indicative of

the usefulness of the standard cost concept and that the perceived

advantages provide a greater level of benefits than the cost of the

disadvantages. Although the standard cost concept is an attempt to link

operational efficiencies to accounting data, it suffers the same

shortcomings as the other two cost concepts by relying on an experience-

based allocation of overhead costs.

2.2 The Changing Organisational and Operational Environments.

The example provided (as illustrated in Tables 2-2, 2-3 and 2-4 as well as

Figures 2-1 and 2-2) is based on the assumptions of a product with an

extensive demand history that remained unchanged in functionality and

materials/components used in its manufacture. Manufacturing operations

have benefited from advances in process technologies. The obvious

outcome is found in improved efficiencies that manifest themselves in

producing more output with unchanged or even reduced resources. Labour

intensiveness is being replaced by capital intensiveness. Regional and

global competition has forced many organisations to reassess their

operations to ensure survival and growth.

64

One of the major changes, however, is the shortened product life cycle in

most industries and as a consequence the need to constantly review the

organisation’s product portfolio. This changing environment has also

changed the information need of management away from operational

efficiency management towards strategic management. Product costs as

well as product introductions and abandonment have assumed a major role

in the managerial decision making process. Furthermore, traditional

operational efficiency measures of cost reduction and capacity

improvement without known consumer demand (increase in inventory build-

up) are replaced by an increasing emphasis on quality production,

customer satisfaction and improved throughput times. The latter concept

is also known as manufacturing cycle time or velocity of production

(Garrison and Noreen, 1994:442). The emerging measure of manufacturing

cycle efficiency [MCE] is indicative of the ratio of value-added time to

throughput time. Ratios below 1 indicate that a number of non value adding

activities are still present in the process and could be targeted for

improvement or ultimate elimination.

Managements have identified a number of organisational efficiency

improvements that need to be complemented by appropriate management

information systems. Whereas in the past management accounting

systems have assumed a major role in the information needs of

65

managements, the reduced emphasis on product cost management and an

increasing requirement for non financial performance measures have

depreciated the value of traditional management accounting systems.

Furthermore, a changing emphasis in operational environments from a

traditional capacity utilisation and unit efficiency strategy towards

continuous improvements, zero inventory management, total quality

management and JIT/FMS has created opportunities and demanded

solutions to incorporate these operational strategies into a composite

information system. JIT (Just-in-Time) is an operational philosophy that

relies on known consumer demand (pull demand) to organise material

resource flows, production scheduling and throughput times. FMS (Flexible

Manufacturing Systems) incorporate computer controlled equipment and

scheduling to complement the task of JIT. While there are a substantial

number of related advanced manufacturing technologies [AMTs], within the

context of this argument both JIT and FMS are treated as generic terms for

the changing operational environments embraced by many manufacturing

organisations. Attempts to develop new management accounting and

operations process technologies have found only limited appeal amongst

practitioners.

66

Although there are a substantial number of testimonials in praise of some

of these new system development the lack of a more widespread adoption

of these systems must reflect on their inability to integrate the information

needs of management. Most prominent amongst these new developments

are: ABC (Activity Based Costing), an extension on this theme ABM

(Activity Based Management), Throughput optimisation or ToC (Theory of

Constraints), Total quality Management and the concept of the Lean

Enterprise [LE]. Each of these concepts and their contribution to the

organisational environments will be discussed in the subsequent chapter.

2.2.1 Activity-Based Costing

ABC developed in response to managements needs for more accurate

product costs. Most organisations formulate their pricing strategies on the

basis of their product costs and the shift from labour-based technologies to

machine based technologies without changing the costing algorithm invited

criticism as to the inappropriateness of single cost driver based overhead

allocation techniques.

The popularity of Activity-Based-Costing [ABC] has largely been founded

on the perceived inadequacy of traditional management accounting

techniques which approach the allocation of overheads as a trade-off

between high and low volume production similar to the notion of a modified

67

system of welfare economics. The underlying concept in welfare economics

is based on the work of Pareto, an Italian economist, who discovered that

optimal welfare conditions exist when the benefit given to one group (or

individual) does not affect the benefits of other groups in a negative way.

His discovery has led to the acceptance of the 80/20 rule in which 20% of

one dimension or parameter explain 80% of another dimension. Application

of this rule can be found in quality control analyses, inventory analysis and

cost analysis for various activities.

The allocation of overhead costs on the basis of a single volume-based

denominator level allows the distribution of overhead costs to individual or

product groups in such a way that the allocation of costs to one product has

no negative effect on the product cost profile of another product. By

negative effect, using the concept of welfare economics, it is understood

that a redistribution of overheads does not increase the overhead allocation

of another product thereby reducing its profit contribution. There is an

obligation on system designers to first evaluate if the current allocation

method conforms to the Pareto principle, in deciding to change from the

current system to an alternative system and evaluate if the Pareto condition

has been maintained or violated. A violation may identify those products

that require assessment as to their retention in the current product mix.

68

If we accept this rule in the allocation of overheads by assuming that the

traditional MAS has been developed along the concept of a modified

welfare economics system, it is possible to construct a total overhead curve

on the accumulated distribution of individual product allocations. Such a

model is likely to display close to Pareto effiency conditions as the

overhead allocation is based on changes in volume cost drivers that

attributes equal proportions to all products within the predetermined

allocation algorithm.

With the introduction of ABC-principles into the cost relevance debate it is

of interest to compare the resultant reassessment and re-allocation of

overhead costs based on operational activity analyses with traditional

allocation techniques to ascertain if the changed product cost profiles have

produced a Pareto improvement towards the efficient (optimality) frontier.

Comparisons as presented in most case studies and testimonials are

difficult to reconcile as the ABC cost hierarchy structure of unit, batch,

product and facility costs (activities) incorporate a proportion of period

costs that are not included under traditional MAS and also display

inconsistencies in the treatment and aggregation of direct and indirect

overhead cost behaviours. Other inconsistencies that have been identified

in the application of ABC systems are the arrangement of costpools under

these (4) category headings which creates conflict situations when other

69

operational strategies are pursued and implemented. The Japanese

innovation of a “lean enterprise” [LE] that promotes the concepts of zero

inventories, J-I-T improvement philosophies [that endeavour to achieve

economic production quantities of (1)] and total quality management [TQM]

amongst others finds it difficult to accommodate the activity hierarchy of

ABC.

These apparent conflicts were recently addressed by Cooper (1996) in

which he defends the relevance of ABC even within the lean enterprise

environment by reference to survey results which indicate that

organisations that have adopted lean enterprise concepts have also

implemented ABC. His defence, however, does acknowledge a number of

shortcomings in the area of batch level activities which he feels are

highlighted by an ABC analysis and sensitises management to carefully

consider the difficulties in implementing LE concepts. Although the

criticism about the relevance of ABC system implementations in certain

operational environments is a welcome addition to the debate of problems

faced by contemporary managements, it further directs attention to the

short term emphasis ABC analyses tends to encourage.

The analysis of an organisation’s activities to understand the incidence of

cost incurrence is a helpful first step but is constrained by the rather limited

70

approach of assessing the ability of current practises and existing systems

to affect changes towards “better” product cost profiles. It therefore is

limited to answer questions as to the relevant product cost under current

operational circumstances. ABC, in such case, may be considered by

management as having only a limited appeal for strategic decision making

as it is not addressing issues of consumer choice and production process

capacities. Poorly designed ABC systems also may encourage

dysfunctional behaviour as mis-specified cost drivers (Datar and Gupta,

1994) have the tendency of directing resources towards activities that are

not clearly associated with the prescribed activities. While there is an

acceptance of the general benefit that can be obtained from ABC analysis

its implementation (similar to traditional MAS) relies substantially on

subjective value judgement and consequently subjectively based overhead

allocations.

A substantial body of literature has reported ABC/ABM implementation

successes, reservations about the benefits (Merchant and Shields, 1993)

of implementation and rejections (Bescos and Mendoza, 1995) of ABC

system implementation.

Such inconsistent testimonials must raise doubts as to the perceived

benefits of changing existing information and control systems. Although,

71

ABC techniques have been promoted as necessary tools for management

decision making activities in a turbulent and volatile environment faced by

most organisations, the evidence for general level acceptance and

subsequent implementation by the majority of organisations reviewed in

anglo-saxon countries indicates a general reluctance for such wholesale

acceptance (Drury and Tayles, 1994; Joyce and Blaney, 1990, Dean et al.,

1991; Boer, 1994; Fechner, 1995). The rationality of the ABC concept is

sound and deserves merit for its attempt to redress the perceived

inadequacies of traditional MAS overhead allocation distortions. However,

the level of reluctance to implement an ABC system, after having expanded

a substantial amount of resources on the initial operational analysis raises

the question as to why.

Some of the reasons suggested by a number of authors that are perceived

as disadvantages relate to additional costs of the system and the necessity

to operate two parallel management accounting systems (as the

requirement to provide financial information to external agencies must

conform to GAAP), thereby questioning the real advantages of an ABC

system, especially as it is perceived to be a more complex system with a

remaining substantial amount of non traceable overhead costs (Kaplan,

1994b)

72

To demonstrate this point: let us assume that the untraceable amount of

overheads after having established activities, cost pools and cost drivers

constitutes 40% (facility related) and that the initial overhead were 30% of

product costs (Drury and Tayles, 1994; Joyce and Blaney, 1990, Dean et

al., 1991; Boer, 1994; Fechner, 1995), then the traceable overhead

component is some 18%. Let us further assume that the company's COGS

is 50% of its selling price we, therefore, may have a margin of error

improvement of 9% (30% of 50%=15% and 60% thereof = 9%) of the

selling price. The additional costs to operate and maintain the new ABC

system would further reduce the improvement in accuracy to less then 9%.

Should the company under review operate at substantially greater profit

margins, the benefit from the implementation of a new ABC system

becomes very marginal indeed. Given this very simplistic example,

nevertheless indicates that the benefits from implementing complex ABC

systems are very much dependent on individual companies within industry

groups (Merchant and Shields, 1993).

Kaplan (1994b) has partially addressed this situation by offering an

explanation as to the reason for the difference between ABC distributed

overhead costs and traditional based overhead allocations. He makes the

distinction by pointing out that ABC systems measure the consumption of

resources whereas traditional MAS measures the resources supplied

73

(stewardship function). His admission as to the non traceable portion of

total overheads and his suggestion to reconcile these differences through

the application of variance analysis and subsequent adjustments reinforce

the observed reluctance by many organisations' management to implement

a new management accounting system as the benefits of such a decision

are at best doubtful.

This doubt by management at the individual or group level provides the

background to their resistance to change as the outcome is uncertain.

Argyris and Kaplan (1994) suggest that extensive research evidence has

shown managements concerted efforts in developing defensive strategies

when threatened by new information or theories that question contemporary

management decision models. They support such contention by relying on

prior research that distinguishes between theories-in-use and espoused

theories. Whereas the former describes the rules that individuals use to

guide their actions, the latter contain the values and beliefs individuals

express when questioned (p.94). The espoused theories can be viewed as

analogous to being "politically correct", to use a contemporary term.

A further problem encountered with ABC system design is the number of

activities, cost pools and cost drivers necessary to establish more accurate

and reliable product related data. Amsler et al. (1993) report that their

initial operations analysis of a company's purchasing subfunction generated

74

42 activities and described the difficulty in finding appropriate cost drivers

for these activities especially as the cost objects were not directly

attributable to specific products. They decided that the complexity

generated by the initial analysis was unmanageable and that a compromise

to reduce the 42 activities to a total of six with three cost drivers was

adequate for improving the overhead distribution accuracy. Such

compromise leads to consequences of error incidence at all levels of the

ABC hierarchy, W hile the error at the unit level may have compensatory

and inconsequential effects (due to the lesser weighting at these levels),

error incidence without compensatory effects at the batch, product and

facility level, however, becomes more pronounced. The issue of

diminishing accuracy and increased error incidence caused by the

consolidation of activities and cost pools has received relatively little

attention.

2.2.2 The Theory of Constraints

The basic assumption that underlies the Theory of Constraint [TOC] is that

every operating system must have at least one constraint or bottleneck.

Identifying a bottleneck situation and remedying its effect on the operational

resource flow will generate a production environment of full capacity

utilisation which must lead to optimal profitability. Such approach to

achieving operational efficiency is in direct contrast to efficiency measures

75

motivated by traditional as well as ABC analysis. Many of the techniques

developed by traditional MAS highlight the inefficiencies of localised

resource wastage (e.g. variance analysis) without considering overall

performance. The notion of capacity utilisation is grounded in the belief that

each individual piece of equipment must be utilised to its full capacity (to

avoid the incidence of idle capacity and subsequent unfavourable volume

variances) to achieve optimum operational efficiencies. However,

equipment acquisition and replacement policies rarely, if ever, consider the

effect their installation into an existing operational environment has on the

other components in the process.

Although linear programming and mixed integer programming [MIP] have

become more accessible with the introduction of fairly inexpensive and

powerful computer technology, these techniques are still in the application

range that is used to solve specific problem situations. A more detailed

discussion and application of the [MIP] technique can be found in Kee, R.,

(1995). While the situation presented appears unrealistic as the identified

Constraint is the number of Set-up hours available, it does nevertheless

demonstrate the value of the [MIP] technique. In addition, if sensitivity

analysis is applied to the situation by increasing the set-up hours available,

profit increases. By systematically reducing the newly identified bottlenecks

in the set of constraint equations we will experience a situation where

76

additional resource requirements reduce profitability. It is this condition

which constitutes a point on the Pareto efficiency frontier and is

hypothesized as conforming to the more general 80/20 rule.

However, the mixed integer approach has the additional benefit of

incorporating sensitivity analyses to evaluate the additional costs incurred

in removing the identified bottleneck. Bottleneck mapping and subsequent

improvement will highlight further bottleneck situations so that a

comprehensive analysis can lead to optimal resource utilisation. As each

successive reduction in bottleneck situations will be accommodated by a

cost/benefit profile, overall process improvements can be determined at the

indifference level. The ability of the [MIP] to sequentially evaluate the

benefits from bottleneck reductions will generate a Pareto optimal condition

which is premised on the notion that optimality is attained when a further

improvement in resource inputs leads to a benefit reduction in an output

resource.

Pareto efficiency in the context of this discussion should not be confused

with the concept of Pareto optimality. Pareto optimality is achieved when

the distribution of goods/services falls on the contract curve in a modeled

Edgeworth-Box diagram and represents the condition of optimal

resource/commodity/welfare distribution. The exchange of goods/services

77

beyond a point on the contract curve leads one consumer to be worse off

in his (her) indifference towards a bundle of goods/services. Although the

concept can also be applied to the production possibility frontier

hypothesis, it is not the purpose of this thesis to deal with the economic

rationale of Pareto optimality but instead to introduce the concept of Pareto

efficiency in which a vital few and not the trivial many affect the output

condition of the firm.

While it is appropriate and possible to develop fairly complex mathematical

algorithms to support the notion of Pareto optimality, it is adequate to

accept the application of the [MIP] analysis in establishing a Pareto

efficiency frontier. Pareto Efficiency frontier in the context of this description

refers to the curvature of the accumulated ranked distributions based on

product demand. This demand can be based on trend analysis of past data

or independent predictions of forecasted data. Many situations involving

two-dimensional mappings have found that the Pareto frontier occurs

frequently at the 20%/80% level, the typical 80/20 rule. Examples of this

application and acceptance can be found at quality control investigations,

inventory control modelling (A-B-C model) and of course in its original

social welfare content.

78

Therefore, if we map variables of revenue against product demand

(volume), product diversity against resource consumption, overhead

accumulation against production volume, etc. we may be able to establish

a Pareto frontier for an organisation’s resource consumption which can be

compared with resource consumption profiles of other competitors and in

the ideal situation of the 80/20 condition may provide an independent

benchmark for comparison. Furthermore, by applying the concepts of the

Pareto frontier it should be possible to evaluate the effect of a modification

to an existing overhead allocation system with that achieved by ABC.

79

2.2.3 Strategic Management Accounting

Ward (1992) suggests that strategic management accounting [SMA] could

be thought of as “accounting for strategic management” whereas Bromwich

(1990) subscribes to the view that it is the “provision and analysis of

financial information on the firm’s product markets and competitors costs

and cost structures and the monitoring of the enterprise’s strategies and

those of its competitors in these markets over a number of periods” (p.28).

Strategic management involves the co-ordination of a complex set of

interrelated activities and therefore requires a supporting management

system that can handle the variety of situations and circumstances

confronting the organisation. Ashby’s Law of Requisite Variety, which has

been applied in Cybernetics, “states that it is impossible to manage any set

of variables successfully with a management system less complex than its

variables” (Hosking, 1993) which is supportive of the current movement

towards increased system complexity through the consolidation of existing

but separated discipline dependent system designs.

Management accounting systems that emphasise the necessity to create

an “accurate” product cost profile are likely to confirm Porter’s (1985)

criticism that “while accounting systems do contain useful data for cost

analysis, they often get in the way of strategic cost analysis” (Partridge &

Perren, 1994:22). The usefulness of the ABC technique to analyse and

80

identify the activities that represent the organisation’s value chain and to

determine the appropriate cost drivers for these activities has been rejected

by many practitioners as too complex and by implication too expensive to

maintain. Although many practitioners accept the need for a revised

Management Accounting System [MAS] and concede that ABC provides

a desirable alternative, their reluctance to implement new systems,

however, must reflect on the perceived disadvantages of ABC. In addition

ABC concentrates on internal operational activities that highlight short term

performance and is not well suited to the longer term evaluation emphasis

required by strategic management. Although ABC concepts are suitable to

analyse activities that extend the value chain from supplier to customer,

they seem to lack the decision support features required for market

positioning of the company’s product range.

The development of a clearly defined competitive strategy is vitally

important in sustaining the organisation’s market position and allowing it to

earn superior profits. Porter’s (1985) competitive advantage classification

scheme of cost leadership, focused strategy and product differentiation

provides a basic concept in developing an action plan to achieve such

sustainable advantage. Cost leadership implies that the value adding

activities of the organisation are lower than any of its competitors. Such

advantages can be gained from economies of scale and scope, internally

81

developed technologies and favourable resource acquisition costs that

must be supported by control systems that provide detailed and frequently

issued cost reports to maintain tight cost controls. This is the domain of a

well-designed ABC system. Product differentiation on the other hand

incorporates action plans that position the product in such a way that it is

highly valued and differentiated by customers on a number of desirable

attributes. These attributes may concentrate on customer service,

availability through widely accessible distribution networks, product

reliability and product design (Fechner, 1995:7).

While the concept of competitive advantage provides a focus for

management action plans it needs to be translated into required resource

capacities and acknowledge the constraints that exist within the

organisational resource boundaries. Here again, a well-designed product

cost system is unlikely to reveal operational inefficiencies that are caused

by less well designed process flow systems. To address this shortcoming

we need additional systems that accumulate and analyse data based on

operational efficiencies. ABC systems are not designed to detect poor

product designs as far as manufacturability is concerned nor are the data

gathered relevant to process flow decisions.

The shift from the traditional cost-plus pricing concept to a target based

82

pricing strategy demands to have a system in place that produces the data

for this changed decision making process. Therefore, the linking

mechanism between strategic management and product costing systems

can be found in the organisation’s operational area. The need to evaluate

both product design and process design in determining target costs

presents an opportunity to incorporate constraint analysis and optimisation

modelling into the domain of traditionally independently treated

organisational activities.

Figure 2-3 illustrates these interrelationships and how the consolidation of

the “accuracy” and “strategy” schools form the foundation of the strategic

management accounting discipline that leads to the determination of an

organisation’s product/service portfolio.

FIGURE 2-3 (Fig. 1-1 repeated here for clarity)

Strategic Management Accounting Framework

1

The case data has been taken from Cooper & Kaplan (1991) “The Design of Cost Management Systems - T ext, Cases, and

Read ings”, 2nd ED.,Prentice Hall , Englewood Cl if fs, pp.291-310. Al though the sample s ize consist of only 44 components out

of 205 0 tha t con stitute the com pone nt inventory of the com pany, it is neverthele ss a usefu l sam ple to demonstrate some of

the overhead allocation changes under the ABC system design.

83

2.2.3.1 Critical Evaluation of Emerging Management Accounting

Systems

2.2 3.2 Case Study Based Comparison between ABC and MAS.

The following case study of John Deere Component Works [JDCW]1

should provide a good example for the comparison of traditional

MAS versus ABC overhead reassignment. The case study provides

detailed data on overhead costs both direct and indirect, material

weights, component demands, batch numbers and quantity and

actual direct labour hours and costs. The data does not include

material costs nor selling prices. As most of the components are

produced for other entities within the corporation transfer prices are

applied that in most cases do not reflect market traded prices. The

objective of the following data analysis is the evaluation of traditional

MA overhead allocations with the modified overhead allocation by

applying ABC techniques to the same data base.

To repeat the assumptions made for the analysis that follows is the

acceptance that a Pareto efficiency frontier exists for any two-

dimensional mapping within the given data. Furthermore, without

having detailed knowledge of the existing constraints (operational

84

bottlenecks) it is impossible to determine the indifference points

(Pareto optimal condition) for the production (or other functions)

process using the [MIP] technique. It is beyond the scope of this

thesis to apply a detailed [MIP] algorithm to the [JDCW ] data

especially in the absence of known production process constraints.

However, it is acknowledged that the decision to expand resources

to reduce or eliminate operational bottlenecks is a management

decision and may fall short of the optimal condition achievable.

Under these circumstances the optimal condition as determined by

the [MIP] approach can be compared with management’s willingness

to limit resource expansion to compute a profitability variance.

A Pareto frontier is dependent on the overall production process flow

analysis and therefore renders individual component capacity

analysis an ineffectual exercise. To an extent this rather liberal

extension of the Pareto principle to other parameters within the

operational context invites a fair amount of tolerance.

Analysing the data from the [JDCW ] case presents the opportunity

to compare overhead allocations on the basis of the traditional

allocation of standard costs based on departmental rates with the

allocation of overheads on the basis of ABC activity analysis.

85

Figure 2-4 depicts the Pareto frontier of the case data by direct

labour hours (product demand based). It appears that the change to

an ABC system based overhead allocation has made some

difference to the overhead distribution of the products. What is,

however, evident from the illustration is that the lower volume parts

have a reduced overhead allocation under the ABC system. By using

the efficiency frontier mapping the argument often used in favour of

ABC implementations is the notion that traditional allocation

techniques disproportionally undercost low volume products.

FIGURE 2-4

Rareto Frontier,sorted by Direct Labour Hours

86

Although cost data for material and direct labour are not included in

the data (given composite data cannot be reconciled with individual

data groups to insure objectivity within the cost groups) comparison,

it is assumed that the ABC system does not change these cost

patterns. Even under the [TOC] these direct costs are unaffected as

a reduction in bottlenecks will reduce total idle time which is reflected

in indirect overhead costs

.

The question that arises from the above data analysis is twofold.

Firstly, can a limited sample from a given population (2050 parts)

adequately reflect the efficiency parameters and secondly, is it

possible to hypothesise that optimal efficiencies will fall within the

Pareto efficiency frontier. In most case studies relationships are

tested using a number of statistical models (the most popular of

these being regression analysis) to support predetermined

contentions. What is suggested by the Pareto frontier approach is to

accept that a notional benchmark situation exists (80/20 rule) and

through internal adjustments and improvements establish whether

this notional Pareto frontier can be matched. This should not be

construed as an attempt to simply accept that each and every

organisation within a given industry is capable of reaching this

efficiency benchmark but given the ability to apply and assess the

87

outcome of a detailed constraint analysis should contribute to

determine the point of indifference. Expanding resources beyond this

point has the effect of creating a Pareto inferior condition as the

additional resources produce a lesser output.

Figure 2-5 illustrates another interesting relationship in comparing

the overhead allocations between the traditional MAS and ABC. It

appears that approximately 50% of the total overhead costs have

overcosted 13 of the 44 products in the sample and of the remaining

31 products 5 show an extremely high percentage of undercosting.

FIGURE 2-5

Product over/under overhead distribution for the JDCW data

88

These 5 products are all in the low volume category and therefore

are unlikely to have a significant effect on the revenue distribution.

While it is conceded that this type of comparison is less acceptable

to the more traditional comparative approaches offered by statistical

techniques, it does, however, provide an alternative comparison that

should contribute to our understanding of the outcome achievable by

changing overhead allocation techniques.

Rather than relying on the visual presentation for asserting that the

achieved redistribution appears to be insignificant, statistical analysis

is a more acceptable method to test this contention. Using a paired

t-test produced the following results (TABLE 2-5) which partially

confirms the data presented in Figure 2-5. It appears, that the ABC

system has identified some of the period costs as overhead costs

traceable to cost objects (indicated by the negative t-values) and the

subsequent allocation has produced statistically significant

differences between the two systems in direct (variable) and total

overhead costs at the 1% level.

89

TABLE 2-5

Comparison between MAS and ABC

overhead allocations

Variable Correlation t-

value

df 2-tail

Sig.

[MAS] O/H direct 0.948 -3.3 43 0.002

[ABC] O/H direct

[MAS] O/H indirect 0.967 -18 43 0.076

[ABC] O/H indirect

[MAS] O/H Total 0.963 -2.9 43 0.007

[ABC] O/H Total

Interestingly, though, the difference in the allocation of indirect

overheads is not statistically significant between the two systems. It

is difficult to interpret this particular aspect of the analysis as the

case data is taken from a limited sample only. If, however, in

subsequent studies similar results are revealed then the promotion

of “better numbers” or improved accuracy on the basis of indirect

overheads only is more difficult to accept. Naturally, an increase in

sample size or preferably using a company’s total product portfolio

(population) increases the validity of such conjecture.

Further analysis of the data by applying a linear regression model to

ascertain if the initial overhead cost allocation under the traditional

standard cost MAS (that were substantially based on direct labour

costs) may reveal a correlation that explains a lesser variance due

90

to other variables than that achieved by the ABC system. The case

detail describes the use of labour run time as the basis for overhead

computations but provides an example in which labour costs are

used in determining overhead allocation rates. Furthermore, a

change in 1984 from a labour cost base only to a multiple base that

included machine hours and Actual Cycle Time Standard [ACTS]

should affect the direct relationship of DLH/overhead incidence and

be reflected in the data. The results from the regression analysis

reveal that the relationship between DLH and Overhead allocation is

the main predictor of overhead costs. It is therefore surprising to find

that the change over to an ABC system shows an even stronger

relationship between these variables. The case study described a

change in the denominator base prior to the ABC implementation

that included machine hours as well as direct labour costs and Actual

Cycle Time Standard [ACTS] to determine overhead rates. Such

change should be reflected in the coefficient of determination (r2)

when the regression is computed by using direct labour costs as the

independent variable.

Table 2-6 shows the results of the regression with total overhead

(MAS and ABC) as the dependent variables.

91

TABLE 2-6

Regression result of Total Overhead

on Direct Labour Costs

Variable $ t value r2 F

O/H

MAS

37.5 21.25* 0.9 451.49*

O/H

ABC

30.9 25.45* 0.9 647.45*

*p< .0001

Reviewing the results in Table 2-6 shows that ABC allocations are

more correlated with direct Labour costs than MAS allocations.

While this finding does suggest a reversal to single cost pool

overhead allocations, it is nevertheless interesting to note that the

perceived benefit from the implementation of ABC is based on only

6.1% overhead allocation attributable to other parameters. This in

itself is somewhat difficult to interpret as the ABC system

implementation was based on (7) distinct activities and (11) cost

pools. The more likely explanation for these results could be the

inappropriateness of applying OLS techniques to such data and

therefore alternative evaluation techniques are required. Again it

must be stressed that this is a single case study and by its very

nature does not allow any meaningful generalisations. It does,

however, provide an overview of the effects an ABC system has on

the cost profiles of individual products. Amongst the other limitations

92

is the lack of data relating to changes in product demand and the

ability of the production process to cope with the possible changed

demand schedules and the appropriate allocation of production

facilities to suit these changes. Therefore, the evaluation of modified

cost profiles as a result of an ABC implementation must assess the

effect on organisational capacities, both production and

administrative, to ascertain if the additional (or lesser?) consumption

of resources has produced the desired improvement in profitability.

2.2.3.3 Error Incidence and System Accuracy

Datar and Gupta (1994) have made a considerable contribution to

the debate with the development of a quantitative exposition

demonstrating the effect of error incidence on the accuracy of total

product cost profiles. The authors present a quantitative model for

identifying the sources of specification, aggregation and

measurement errors that are a consequence of the complexity in the

design and implementation of an ABC system. The authors further

suggest that the likelihood of an inverse relationship between

specification and aggregation errors on the one hand and

measurement errors on the other hand is an outcome of increased

system complexity. They define:

93

specification errors arise from the choice of cost driver which

does not reflect the demands placed on resources by

individual products, the case study presented by Amsler et al.

(1993:568) provides clear evidence of this situation;

aggregation errors occur when costs are aggregated in single

cost pools although the activities these costs reflect are not

homogeneous. Cost pools that accumulate costs from

heterogenous activities arise when individual products use

different amounts of resources across cost pools, again the

case presented by Amsler et al. (1993:568) provides a good

example;

measurement errors are related to identifying costs within a

particular cost pool and measuring the specific units of

resources consumed by individual products Amsler et al.

(1993:568).

The contention of the Datar and Gupta (1994) paper and others,

(Grunfeld and Griliches, 1960; Lim and Sunder,1990, 1991) is that

the attempt by ABC system designers to reduce the incidence of

specification and aggregation errors (by implementing more activity

specific cost pools and activity specific cost drivers) will increase the

level of measurement errors. The gravity of the measurement error

on the product cost accuracy is a consequence of better specification

and greater disaggregation suggesting that less rather than more

complexity is required for the improvement of overall product cost

accuracy.

94

The authors further suggest that with the incurrence of transaction

and implementation costs, these multiple cost pool systems are

unlikely to capture both diversity and complexity of activities that give

rise to such costs particularly as these and other cost groups cannot

be directly related to cost objects (products).

Therefore, companies should exercise some care during the

analytical stages when identifying and defining cost categories such

as facility related classifications of general and administrative

expenses, rates, taxes, etc. that are difficult to associate with product

specific resource expenditure.

TABLE 2-7

Error Incidence in [ABC] Product Costing Approach

[ABC]

ACTIVITY

LEVEL

COST

DRIVER

COST

POOL

ERROR

INCIDENCE

UNIT determinable specifiable specification

BATCH determinable specifiable aggregation &

measurement

PRODUCT partially

determinable

partially

specifiable

specification,

aggregation &

measurement

FACILITY not-

determinable

difficult to

specify

aggregation &

measurement

95

Table 2-7 provides an overview of the ABC activity levels and the

type of error that is likely to be the consequence of reduced system

complexity. The assumption that the greater the disaggregation of

cost pools and the larger the number of activities identified must

result in greater accuracy of product costs is a misconception and

may help to explain why some of the reported testimonials in various

literature have concluded that the desired outcome, a successful

ABC system implementation, has failed to materialise. The natural

tendency by management to treat new theories and techniques with

healthy skepticism (Argyris and Kaplan, 1994) seems to be partially

supported and justified.

If the proposition of an inverse relationship between complexity of an

ABC system and desired levels of accuracy is accepted, it should be

possible to determine a trade-off value or point of indifference.

However, to determine an optimal level of system complexity some

of the parameters required in the development of such a model must

either be known or must be able to be determined deductively.

Babad and Balachandran (1993) have presented a quantitative

approach to compute an optimal number of cost drivers and an

aggregation of cost pools to determine the trade-off between the cost

of information (transaction recording, data base maintenance, etc.)

96

that evolves as a consequence of complex and detailed ABC system

design and the level of accuracy that produces improved product

cost information. The sacrifice in trading off some accuracy and

therefore an increase in the incident of specification and aggregation

errors should also be balanced against measurement errors.

Finally, the eventual system design should be compared with both

the ABC benchmark (optimal complexity) product costs and the

traditional MAS derived product costs. Only by using the criteria of

error incidence reduction/increase as well as the additional

information related cost incurrence of a fully developed ABC system

does it become feasible to quantitatively compare the cost/benefit

profile of abandoning the existing traditional MAS and implementing

an ABC system on the premise of "more accurate" product cost

information.

The diagramatic presentation depicted in Figure 2-6 adopts the

quantitative details of a relatively simple reported case study

(Pattinson and Arendt, 1994) that limits its analysis to the

disaggregation of a single cost pool of existing overhead costs.

However, this case study (like most other reported testimonials)

suffers from the omission of system related additional transaction

97

and bureaucracy costs which are the by-product of ABC system

implementation and maintenance. Rather then relying solely on a

quantitative comparison of overhead costs established through a

traditional MAS database it proves to be more helpful to provide an

additional graphical analysis that incorporates error variances and

additional system costs on a conceptual basis. The probable cost

behaviour curve for the additional system costs involved in

implementing an ABC system is hypothesised to be linear as the

number of products included is limited to three.

The case study also reports a number of difficulties that were

encountered in establishing the appropriate level of complexity in the

implementation of an ABC system. Although the report analyses a

support function (supply-procurement) of a manufacturing

organisation it reconciles the cost profiles of the traditional MAS with

those of the initially proposed and subsequently accepted modified

ABC system. Such reconciliation is useful as it does not pollute the

original cost estimates or the actual cost reported by the accounting

system.

98

Further, it is of interest to note the reported misgivings by a number

of departments in accepting the complexity of the initially proposed

ABC system, even though it was intended to implement the new

system in the procurement department only. While there was

evidence of resistance to change by most of the departments

involved with the recording of new transactions, estimating the cost

of the new activities and the maintenance of the database,

departmental personnel agreed not to continue with the existing

traditional based MAS and accepted a modified and substantially

aggregated ABC based system.

A common theme of questioning the benefits from the

implementation of the initially proposed system is related to the

additional effort required in supporting the ABC system, the

additional costs and resources that would be incurred and the ability

by manufacturing personnel to manipulate the system in ways that

allowed redistribution of product line costs to other products. The

latter reason (the motivation for cost manipulations provided by the

new system) for the reluctance by departmental personnel to accept

the new system was not evidenced as a disadvantage of the existing

system. The authors offered a number of explanations for the failure

to accept the initial ABC system that can be summarised as follows:

99

- lack of involvement by all departments affected by the new

ABC;

- initial complexity created a resistance towards change and

could have been moderated by a less complex system to be

modified and adjusted after implementation;

S a new ABC system introduced as a better management

accounting system is perceived as not addressing the

performance measures to satisfy the user groups' information

needs;

- the determination of activities and cost drivers must be

complementary across functional support groups.

The case study report also supports the contention of Babad and

Balachandran (1993) that cost pool consolidation has a limited effect

on the numerical accuracy of product cost profiles. The data used in

Table 2-8 is taken directly from the case study and slightly modified

to generate the graphical presentation of Figure 2-6.

100

TABLE 2-8*

(Product data taken from Pattinson and Arendt (1994:61))

Product Product-Charact. Traditional

MAS

ABC-

complex

ABC-

modified

A High Volume $ 10,227.00 $ 5,996.00 $ 6,146.00

B High Vol./Complex $ 8,513.00 $ 6,413.00 $ 6,612.00

C Low Volume $ 2,886.00 $ 9,217.00 $ 8,868.00

MAS set to

zero

Change from

MAS

Change

from MAS

A High Volume $ 0.00 -41.37% -39.90%

B High Vol./Complex $ 0.00 -24.67% -22.33%

C Low Volume $ 0.00 219.37% 207.28%

*for details or numerical example and detail computations refer to Pattinson and Arendt. 1994

The cost curves in Figure 2-6 depict the overhead allocations under

traditional MAS represented by the horizontal line at the zero level

(base line), the initially proposed ABC system (termed here as

benchmark cost curve) and the accepted modified ABC system

(indicated by the modified ABC cost curve). Although the case data

includes only (3) product lines and therefore variances between the

two ABC systems and the traditional MAS are contrasted with this

limitation in mind, the evidence clearly identifies the area of the

aggregation error as defined by Datar and Gupta (1994).The

movement of both under and over costed areas towards the baseline

is logically defensible as the consolidation of cost pools to the

original level of perhaps one used by the traditional MAS would

result in no error variance.

101

FIGURE 2-6

ABC compared to Traditional MAS Product Cost Portfolio

Specification errors are more difficult to identify with only (3) product

lines under consideration but would be expected to increase with the

number of products within the total portfolio. As the number of

products increase it is likely that the intersection point between under

and over allocated overhead costs changes along the horizontal cost

curve of the traditional MAS line thereby shifting the balance of under

and over allocated cost proportion. Predicting the shift of the

intersect is dependent on both product complexity and volume

production, however, intuitively specification errors would increase

102

with product complexity and production process complexity. Such a

proposition requires empirical investigation to test the validity of this

assumption.

Resource consumption for system expenditures in the form of

transaction and bureaucracy costs will have their own economies of

scale and scope and an increase in product numbers will change the

small number product portfolio's linear system costs to a non linear

cost behaviour for larger number product portfolios. .

2.2.3.4 The (IR)Relevance of Cost Management Systems

Differences between MAS and ABC can be attributed to the

treatment of overhead cost allocations. While the traditional MAS

has been criticised on the basis of trade-offs between high and low

volume products by using a single volume based cost driver, ABC,

on the other hand, is based on the identification and analysis of all

activities that contribute to the productive effort and the designation

of appropriate cost drivers for each of these activities to establish a

highly disaggregated overhead contribution matrix that is presented

as a more accurate product costing system. A further assumption

that is promoted as a necessary precondition for the changing of the

cost management system has been the notion of increasing

103

proportions of overheads as proportion of total product costs. This

myth has been dispelled by survey evidence (Whittle, 2000; Boer,

1994) as a generalisation to affect all industries.

Earlier in the discussion the concept of the LE was introduced to

highlight the efforts that are being made to reduce economic batch

production to single digits which, as a logical consequence, would

require an increased number of set-ups for each product. The trade-

off between an increasing number of set-ups per product must be

balanced with the available resources for this function. Here the

assumption is that a reduction in individual set-up times can be offset

with the increased number of set-ups. While this change in

production process strategy is desirable in reducing customer waiting

times, it must also be balanced against the achievement of optimal

profitability.

The example that follows is based on a number of generalised

assumptions that are necessary to provide the analysis. Each of the

four products with its associated data (hours of production

processing) in the example is based on an achievable average

learning curve coefficient and in addition the set-up times are shown

as independent sequential. The latter aspect is of some relevance as

104

in certain situations set-up sequences for certain products may offer

lesser times than for other sequences. For example, if product C is

scheduled to follow product A, set-up times maybe lower than when

product C is scheduled for production after the completion of product

D. Other uncontrollable events such as machine and labour

availability have been considered by using period averages for these

data.

Table 2-9 presents the product data details for (4) products that are

representative of a typical product data information sheet. The

marginal contributions of each product have been calculated (Table

2-9a) using different cost driver selections in each of the three cost

pools (Table 2-9b).

105

TABLE 2-9, Product data*1

*1 Unit cost data has been calculated by dividing the activity cost shown in Table 2-9b for

each of the four products by the respective product demand. Percentage computations

are based on using the unit level ABC costs as base for deviations of all other marginal

and unit overhead calculations.

106

TABLE 2-9a

Product cost and contribution margin data

Notes to Table 2-9a: Inventory details of the company are presented in Case-study 4.3,

p.166. Product data has been modified from original data obtained from

company records. Furthermore, only four products have been selected

to exhibit the difficulties that existed in selecting an appropriate cost

driver for three of the cost pools used by the organisation. The

accumulation of costs in the identified cost pools was established after

some analysis as to homogeneity of these costs. Whereas the cost

pools for set-up and quality control may be classified as batch level

costs, the planning cost pool could include some product level costs.

However, the purpose of the exhibit is to clearly establish that the total

cost in each of the cost pools remains unchanged regardless as to

specification changes of cost drivers. The consequence of such

constant cost pool is that changes in activity costs have no effect on the

total contribution margin. This fact raises the question as to which of the

proposed cost accounting systems provides management with the most

accurate cost. While there maybe an argument for individual product

analysis to establish viability, the optimisation of resources or the

identification of operational constraints remains unaffected by the type

of overhead distribution (allocation) system employed by organisations.

107

TABLE 2-9bCost Pool data using different cost drivers

108

Table 2-10 shows the computation details to calculate different

product costs using a number of different cost drivers. The benchmark

costs have been determined as the most complex, most

disaggregated ABC system in which cost pools contain homogenous

costs and cost driver selection is based on resource consumption by

causal effect. However, as Datar and Gupta (1994) point out, these

costs are difficult to obtain and in most firms remain unobtainable. All

costs included in the cost pools are considered variable in proportion

to the volume produced as any fixed costs that could be attributed to

these cost pools are likely to be treated by cost management systems

as facility level costs (ABC) or period costs (MAS). Furthermore, even

if it would be possible to distribute all overhead costs to cost pools, the

outcome would remain unchanged.

TABLE 2-10

Example (Set-up cost pool) of individual product

activity cost calculations

Product Set-up Turn. Mach. Drill Assy Computations

A x1 y11 y12 ... y1j Product AABC = 3x1 y1j zj

B x2 y21 y22 ... y2j Product BHRS = (3x2 y2j / TH) TC

C . . . . . Product Cno = (x3/ 3xi) TC

D xi yi1 yi2 ... yij

Direct

Labour

Cost

z1 z2 ... zj Total Hours (TH) = 3xi yij

Total Cost (TC) = 3xi yij zj

Also included (refer Figure 2-7) are the traditional MAS allocations

using a single driver (either direct labour hours [DLH] or direct

109

machine hours [DMH]) to demonstrate the level of difference for each

cost driver selection by indicating over or under allocations. The

product data shown in Table 2-9 has been submitted to a constraint

analysis (LP application) to determine the most efficient consumption

of resources given prevailing capacity constraints. The model is based

on the following constraints equations:

TABLE 2- 11

Constraint Equations

Product A B C D Constraint Unit

DLH-ASSY 0.025 0.025 0.025 0.05 <= 8000 Hours

DMH -Turning 0.05 0.05 0.05 <= 8000 Hours

DMH -Machining 0.025 0.1 0.05 <= 10000 Hours

DMH -Drilling 0.025 0.1 0.025 <= 10000 Hours

Batch S ize 1 = 500 Un its

1 = 1000 Un its

1 = 400 Un its

1 = 500 Un its

SET-UPS 1 <= 250

1 <= 250

1 <= 250

1 <= 250

SET-UP (TIME) 1 1 1 1 <= 3500 Hours

QC (TIME) 1 1 1 1 <= 2500 Hours

PLANNING (TIME) 1 1 1 1 <= 3000 Hours

Product Demand 1 >= 0 Un its

1 >= 0 Un its

1 >= 0 Un its

1 >= 0 Un its

Product Margin (ABC) $10.19 $15.54 $14.96 $23.63 =Objec tive Funct ion (max)

The resultant computational values are shown in Table 2-12 also

indicating shadow prices which reflect the benefit (additional profit)

available by relaxing the identified constraints. A further assumption

that underlies the model is that the computed product mix does not

exceed the individual product demand. For example, increasing the

available labour hours in the assembly section would increase the total

contribution margin by $450.00 for each additional labour hour.

110

FIGURE 2-7

Activity Cost Variation[Benchmark - ABC]

The resultant computational values are shown in Table 2-12 also

indicating shadow prices which reflect the benefit (additional profit)

available by relaxing the identified constraints. For example,

increasing the available labour hours in the assembly section would

increase the total contribution margin by $450.00 for each additional

labour hour. A further assumption that underlies the model is that the

computed product mix does not exceed the individual product

demand.

111

TABLE 2- 12

Results report of LP analysis

Solution Cell Starting Final

Total Contribution Margin ($1,010,168.00)$4,209,320.00

Prod. Demand A 1.00 8000 Prod. Demand B 1.00 68000 Prod. Demand C 1.00 60000 Prod. Demand D 1.00 92000

Answer Report Value Constraint Binding? Slack Dual Value

Prod. Demand A 8000 >=0 No 8000.00 0 Prod. Demand B 68000 >=0 No68000.00 0.00 Prod. Demand C 60000 >=0 No60000.00 0.00 Prod. Demand D 92000 >=0 No92000.00 0.00

DLH-ASSY 8000 <=8000 Yes 0.00 450.00 DMH-Turning 8000 <=8000 Yes 0.00 79.00

DMH-Machining 10000.00 <=10000 Yes 0.00 72.00 DMH-Drilling 10000.00 <=10000 Yes 0.00 142

As presented in Table 2-12, the current constraints are concentrated

in all of the production areas suggesting an increase in direct labour

resources through the introduction of a second shift or employment

of additional operators would increase total profitability by the

amounts shown under the dual value column.

Product margin computations have been applied under a number of

different assumptions that include different cost drivers for each of

the defined cost pools. W hile the contribution margins vary

considerably for each of these assumptions (refer to Table 2-9a),

there is no change in optimal profitability. The explanation for such

rather unusual circumstance is based on the fact that the overall cost

within each cost pool remains constant and, therefore, has no effect

on either the capacity constraint calculation or the optimal product

112

mix given the available resources. Furthermore, it supports an

argument for static product mix determinations based on capacity

constraints rather than marginal analysis. In addition, make versus

buy decisions that are also based on marginal analyses and relevant

cost concepts should be reviewed on the basis of product mix

changes and their resultant change in capacity utilisation. Any

analysis based on individual product contribution and subsequent

decision to channel additional resources to the most profitable

product may not result in increased profitability nor is it likely to affect

any of the currently identified constraints. However, what has

become apparent is the limitation any individual product contribution

analysis presents in determining the most appropriate distribution of

available resources.

While the application of the optimisation model was based on

production constraints to determine the optimal product mix (given

a minimum demand for each product to be greater than 0) the model

can be respecified to use product demand as the input variable to

determine the resources required to accommodate that demand. The

model is based on the assumption that the organisation operates as

an entity within a product market where the market demand remains

unaffected by the product supply of the individual organisation. A

113

variation of the model to test for maximum profitability was the

sequential reduction in product demand of one of the four products

to zero (refer Table 2-13). When product A was set at zero overall

profitability increased to $4,216,615 (Alternative 1). All other

permutations produced lower profit amounts when compared to the

initial four product mix solution of $4,209,320 (Alternative 5). The

latter application would complement the strategic-based product mix

choice and focus attention on improving process efficiencies and

capacity optimisation. However, the question as to the most

appropriate product mix choice given the conflicting results of the

product mix permutations (alternative 1 > alternative 5) must be

resolved. Such an impasse can be resolved by reviewing the shadow

prices for each of the solutions and choosing the alternative with the

largest total shadow price (opportunity cost).

TABLE 2-13

Profitability under varying product mix selections.

PRODUCT DEMAND (UNITS)

Alternative Profit A B C D

1 $4,216,615.00 0 70770 58462 95385

2 $2,872,400.00 0 0 80000 80000

3 $3,776,112.00 59250 85188 0 87781

4 $2,641,083.00 69333 37333 90667 0

5 $4,209,320.00 8000 68000 60000 92000

114

By analysing the shadow prices for each of the alternatives as shown

in Table 2-14 and aggregating these prices for each of the

constraints identifies the most desirable alternative. As Table 2-14

demonstrates alternative 1 has a total shadow price of $737 whereas

alternative 5 produces a shadow price of $743 and all other

alternatives contribute substantially below these levels.

TABLE 2-14

Opportunity costs under different product mix constraints.

G137

Altern.

Function

1 2 3 4 5

Resource

Demand

Opport.

COST

Resource

Demand

Opport

.COST

Resource

Demand

Opport.

COST

Resource

Demand

Opport.

COST

Resource

Demand

Opport.

COST

ASSEM BLY 8000 $511 6000 8000 $600 4933 8000 $450

TURNING 7692 8000 $ 580 7352 8000 $ 244 8000 $ 79

M ACHINING 10000 $ 48 4000 10000 $ 70 10000 $ 192 10000 $ 72

DRILLING 10000 $178 10000 $ 40 4324 10000 $ 112 10000 $142

Opport. Cost $737 $ 620 $670 $ 548 $743

While the difference between alternative 1 and 5 is marginal, it is

nevertheless indicative of the most beneficial strategic choice to be

made by the organisation if the overriding objective is considered to

be profit optimisation. The example was based on the assumption

that the organisation’s main objective is the improvement in

shareholder value by offering a product mix that produces optimal

profits. It has been demonstrated (refer to Table 2-9b) that the cost

management system employed is irrelevant in influencing the

115

outcome. Although each alternative has produced different total

costs associated with each cost pool, the overall variable overhead

costs under each cost alternative have remained constant. The

marginal contribution of each product under each of the six cost

management approaches has displayed substantial variation but

does not affect the production process in achieving optimum capacity

utilisation.

The latter outcome is supporting the concepts underlying the TOC. It

is clearly a function of total capacity (resource) utilisation that

determines optimal profitability rather than the idea that marginal cost

analysis or a more accurate cost system leads to improvements in

profitability. Product design and manufacturability are more important

concepts in the determination of optimal profitability and provide

strong evidence that cost accounting systems are largely irrelevant

in achieving this overall objective.

Although the previous example served as demonstration of

emphasising the effect, or lack of effect, on an organisation’s optimal

profitability using a manufacturing organisation’s data, similar

application conclusions can be drawn when the analysis uses a

service organisation to determine profit or service optimality. What

116

changes, however, for service organisations is the definition of

appropriate cost pools as well as defining the level of capacity for

various activities. An initial activity analysis will assist in the

determination of both appropriate cost pools and definable activities.

Furthermore, the case study presentation and analysis in chapter 4

deals with two service type organisations that include a profit oriented

institution (Stock Exchange) and a number of non profit organisations

(various Australian universities). Although, this analysis does not deal

with the specific determination of cost pool identification to compute

capacity optimisation, it is, however, reasonably simple to extend the

previous example to formulate appropriate parameters for these

service organisations.

117

2.3 Chapter Summary

The presentation and discussion together with some critical commentary

on a number of cost accounting techniques have culminated in the

proposition that any of these systems will not influence the organisation’s

optimal profitability. Such proposition is based on the assumption that an

organisation’s product portfolio must be submitted to a resource capacity

optimisation (constraint analysis) rather than relying on individual product

marginal contribution analysis for managerial decision making.

Although the proposition of cost management system indifference is

interesting, the need to develop individual cost profiles remains a

requirement for other organisational obligations. The choice of cost

management system, however, should no longer be considered a

prerequisite for improved profitability.

The continued popularity of simple overhead allocation techniques seems

to support the proposition of indifference. However, the choice of cost

management system may depend on other factors. One of the factors that

must be considered is the accuracy and integrity of the existing data

acquisition system. Data base accuracy is a major concern for any system

that relies on existing and prevailing data to develop prediction models as

aids for managerial decision support systems. Such pre-requisite applies

118

equally well to production based and service organisations. The distinction

in the application between these two groupings must be found in the

identification and determination of relevant model parameters.

The following chapter develops a model that is capable of detecting data

base accuracy and integrity, Furthermore, the model can be applied to

allocate overhead costs on a more relational basis that is complementary

to the organisation’s specified criteria for product cost profiling.

119

3. Model Development.

3.1 Introduction

Although in the previous chapter it was argued that cost management

systems have only limited relevance in determining an organisations

optimal profitability, a cost management system, however, is necessary to

determine profitability in the first place. While the reliance on single volume

cost drivers can produce some distorted cost profiles, its simplicity,

however, seems to be one of its perceived major benefits as evidenced by

a substantial number of survey results (W hittle, 2000) attesting to the

continuing popularity of the absorption cost system. Rather than developing

a complex system of cost aggregations to ascertain a more “accurate”

product cost, it is more likely that organisations will benefit from a less

complex cost distribution system that is based on the organisation’s

production and revenue pattern.

Anecdotal evidence suggests (Koch, 1998) that almost all data bases that

represent the population of data items of interest follow a non linear pattern

when ranked on a two dimensional criteria. What’s more the pattern often

identified follows the Pareto principle or the 80/20 rule. This generalised

distribution has been popularised in 1950 by Joseph Juran who observed

that in many applications the vital few, not the trivial many, accounted for

the majority of problems related to quality of output. Since then the Pareto

120

principle has often been referred to as the 80/20 rule or A-B-C analysis (or

classification). A well known application of the A-B-C classification within

the accounting domain has been in inventory control system design.

Identifying products on the basis of their individual value in relation to the

total value of inventories provides a sound approach for determining the

resources to be expanded in controlling a major asset in most

organisations. An extension to this product classification as to the individual

product value within the total product portfolio would be to analyse if the

product cost profiles follow a similar distribution with particular emphasis

on the overhead proportion. While it is hypothesised that the resource

consumption of products parallels this of the inventory classification

ranking, normal statistical analysis should support such conjecture.

However, the simple ranking of data base items to confirm the existence of

a Pareto distribution that displays a cumulative upward sloping curve

provides limited benefits for predictive computations of the variables

selected.

To utilise the identified Pareto curve or Pareto frontier, the development of

a model that mirrors the Pareto frontier of a given data base would provide

the computational foundation to calculate point estimates that are

consistent with the Pareto frontier. The Generalised Pareto Distribution

(GPD) was first introduced by Pickands (1975) and has the following

distribution function:

121

...................................(1)

where a = positive scale parameter

k = shape parameter

the density function for the GPD is:

.......................................(2)

where a and k are as before the scale and shape parameters. This model

is often applied to compute values for extreme distributions in both the fat

and long tail to predict future occurrences of interest. To utilise the GPD

both parameters a and k need to be calculated by reference to the

underlying data sample. It is obvious that the computation of these

parameters is critical for the predictive ability of the model but is limited to

point rather than incremental value estimates.

Extensive literature research did not reveal the existence of a model that

incorporates the characteristics necessary for the prediction of variables of

interest. Mathematical modeling of data base patterns constitutes the

primary step in the model development, followed by statistically testing the

“real” data base pattern against the model generated values. Rather than

relying on the extensive anecdotal evidence provided and discussed by

Koch (1998), data analysis approaches of random number generated data

122

bases as well as publicly available data bases will be investigated to

establish a consistent data item pattern that produces a Pareto frontier.

A further benefit expected from the data base analysis strategy is a

consistent pattern or Pareto frontier over a number of periods within the

investigated domain. Although anecdotal evidence is not available to

support this proposition, inductive reasoning from many case study details

presented by Koch (1998) would strongly support such hypothesis. Should

this phenomena prove to be correct then the model can also be applied to

identify data base inconsistencies that are caused by recording errors or

omissions of data item details.

3.1.1. Database Integrity

While literature in general acknowledges the existence of data base errors

(Valenstein and Meier, 1999) through faulty recording as well as detail

omissions, there seems to be limited empirical evidence to support this. It

also appears that most of the studies concerned with error entries is

reported in the general medical and associated literature. The concern

amongst medical professionals is often related to the treatment and test

ordering of patients as any erroneous record could lead to eventual

litigation. Some additional evidence is provided by Grasha and Schell

(2001) in an experimental setting to test the incidence of error entry and

123

product selection errors by a group of undergraduate students of mixed

gender. The presumption made by these researchers is the general modal

rate of error incidence of between 3% and 5% in the pharmaceutical

domain of prescriptions filled. However, Grasha and Schell (2001:53) claim

that “Sequential, self-paced, repetitive tasks whereon the output of one part

serves the input for the next component are very common.” and list a

number of examples including the filling of warehouse orders. The filling of

warehouse orders has a number of distinct sequential tasks starting with

the acceptance of the order either through verbal communications

(telephone acceptance) or electronic based entries (e.g. web based) and

completing the cycle by picking the items and shipping them. Data entry is

mostly via keyboard into the local inventory data base from which a picking

slip is produced to initiate the order picking and subsequent shipping cycle.

At each of these sequential data entry and item picking steps error

incidence will occur at lesser or greater levels depending on the internal

control systems employed by the organisation.

Surprisingly, there is very little literature in the auditing arena devoting

empirical research to data base integrity, although similar consequences

as those anticipated by the medical profession could be anticipated by the

auditing profession. However, one reason for the paucity in data base

integrity research within the auditing domain maybe the regulated ability to

124

declare detected deviations in recorded data only if these deviations

exceed materiality limits. In many cases the materiality concept requires

deviation reporting if the differences in recorded data varies by more than

10% from factual situations. A good example are inventory record

deviations from physical counts.

In subsequent sections of this chapter the basic framework for the Pareto

frontier model is presented, the results of the developed model’s generated

values against both the random number generated data bases as well as

the publicly available data bases are statistically evaluated to confirm both

pattern consistencies and model robustness. An additional advantage of

using computer generated data bases is the avoidance of entry as well as

omission errors. The final section will discuss some of the limitations of the

model as a predictor of future pattern analysis.

125

3.2 Development of A Pareto Frontier Model.

The characteristic of the Pareto distribution clearly represents a non-linear

relationship between two variables of interest. As such, models like the

general decay/growth model, the learning curve model, the economic

average total cost curve model, as well as the GPD model as shown in

equation (1), serve as a good starting point for the development of a Pareto

(Pareto frontier) model. W hile the GPD model incorporates both shape and

scale parameters, the computations are concerned with point estimates of

data elements at the long and fat tail regions of the distribution. Such

limitation is too restrictive for the current research question and a more

relevant starting point for the development of the model criteria can be

found in the typical form of a negatively sloping exponential model that is

presented in the following functional relationship:

In addition, the model must meet some specific relational criteria between

variables one and two. The question that arises, however, concerns the

validity of developing a model for the computation of point estimates of an

existing data base that provides an accurate representation of the

distribution of the individual elements. While it may be inappropriate to

employ a model for the calculation of individual item contribution to verify

126

an unbalanced distribution, when it concerns the verification of overhead

cost allocation, the need for comparing an existing allocation against an

impartial benchmark is justified. The reason for the latter argument can be

found in many practical applications where initial recording of prime cost

items produce substantial variances against a preset standard. The

traditional management accounting system has been criticised because it

allocates overheads on a single cost driver based volume approach which

leads to prime cost variations that are likely to amplify the misallocation

problem.

Most Pareto based modeling is accomplished by analysing data bases to

establish distributional characteristics that complement a desirable

criterion. These evaluations rely on access to data bases that represent the

total population of elements of interest. An example of such approach is the

ranking of inventory items on the basis of total item value in descending

order. Such approach can be denoted as x1$x2$x3.......$xn. Coordinate

pairs (xi,yi) are then computed by equation (4). Simple cumulative

calculation of individual item proportion being added to preceding items

within the sequence will produce an upward sloping continuous (without

inflection points) curve starting at the origin (0%, 0%) and terminating at the

terminal data pair (100%, 100%). The general form of a cumulative model

is shown below::

127

where yi cum = cumulative percentage of the i th item in the data basexi = ith individual item

n = total population of data base

The first term on the right hand side computes the item’s individual

percentage contribution while the second term represents the cumulative

value of all items preceding the ith item. To accomplish the analysis of

population data bases, standard spreadsheet applications can be utilised

to establ ish an initial computational data array that consists of the

parameters required to compute item contributions that mirror a typical

Pareto or unbalanced distribution.

Three (3) pre-determined data points must fall on the aggregated data

curve which are the origin (0%, 0%), the reference criterion (20%, 80%) and

the terminal value (100%, 100%). Although the initial or origin of the Pareto

distribution is constituted by the this point estimate, the first data pair (x1,y1)

however, is the point estimate of origin and becomes part of the modeling

process to determine the model parameters. The initial model developed

takes the following form:

2The ? In the 20/? refers to a parameter choice in the i terat ion process as the assumption of a third undetermined focal

poin t on the pare to fron tier c ann ot be ass um ed to be c ons istently at the 8 0% level on the y axis.

128

where a = constant term (obtained through iteration process given PT)PT = total number of products in portfolioxi = ith product rank within portfolioyi cum = cumulative percentage of ith product contribution

Again, note as commented for (4), the first term on the right hand side

computes the product’s individual percentage contribution while the second

term represents the cumulative value of all products preceding the ith

product.

While the Pareto model depicted in (5) allowed computations to determine

the focal 20/80 data point it was, however, more difficult to determine the

value for the very first data pair in a given data base. As the main purpose

of the model is to provide a standard Pareto frontier that allows item

comparison of an existing data base, it is necessary to specify both the

(20/?)2 data pair as well as the first item contribution. The terminal

(100%/100%) data pair is a consequence of the common denominator

which by the logic of the equation will always be unity. Testing of the model

against a variety of different generated data bases revealed a weakness

3

For a m ore detailed discuss ion on W eibull distribu tions refer to Duf fy, S .F., and Baker, E .H., “W eibull Param eter

Es timation - Theory and B ackground Inform ation”, http:// www.csuohio. edu/civileng/ facu lty/ duffy / Weibull

_Theory.pdf pp. 1-22.

4

Notation of the base for the natural logarithm varies from exp to (e) only. This thesis adopts the convention of

abbreviated descriptor.

129

that produced inconsistent values for the first item contribution when the

constraint was equated to the value of the first item in the “real” data base.

To overcome the model’s inconsistency (lack of robustness under changing

parameters) a more robust model development was necessary. Although

a number of sample inventory data bases from a current research site were

used for model mapping and item comparison, the relatively small number

of these data bases (inventory records for 7 years) was insufficient to

provide the necessary confidence level for the general model. The original

data bases were used as input data in a curve fitting software application

to establish the best fit of the non linear characteristics of the data base.

The W eibull3 model consistently produced the best fit with the highest

correlation coefficient and the lowest error term. The standard Weibull

model consist of the following terms:

where a,b,c and d = are parameters that are calculated and become constants fora given data base.

e4 = base of Napierian or natural logarithm (2.718281)

While the Weibull model mimics the curvature of a typical Pareto

5

T he model shown here was developed through extensive use of Spreadsheet based optimisation functions and

automated macro applications. W hile these are obtainable from the author, they are still in a developmental stage

and w ill be incorporated into a functional software package in the near fu ture.

130

distribution it has only limited robustness in computing point estimates.

Furthermore, the computed point estimates must be aggregated to

establish a cumulative distribution presentation. Through continuous

iterations of the unknown parameters (initially they set at 1) values for each

of these are ascertained. Experimentation with the basic model

(mathematical modelling process) and inclusion of the base variable

metrics (x) produced the following model5:

where P = total number of products in portfolioxi = ith product rank within portfolioyi cum = cumulative percentage of ith product contributionc = constant for a given data base.(xi/P)d = term that determines the shape parametere = base of natural logarithm (2.718281)

As the Weibull model is normally applied to failure data (materials) and

therefore has a minimum data pair, the inclusion of a constant term (a or ")

is necessary for the prediction of material characteristics. Furthermore,

such a prediction model, similar to ordinary linear regression models,

analyses sample data to infer characteristics or attributes of the population.

131

To apply Pareto analysis to a data base, however, is based on the data

availability of a population. Therefore, as both initial and terminal data pair

values are known, the inclusion of a constant term representing the

intercept at the lower limit of the relevant range is irrelevant. The main

purpose of the model (5, 7) is to calculate point estimates for any item

within the data base and compare it with the curvature of the actual

distribution. The assumption made to defend this proposition is based on

the model’s ability to mirror the data points of the original distribution with

minimal deviation and the proviso that a data base comparison between the

“real” random data base and the model computed data base reveals

statistical insignificance. If the statistical analysis confirms this proposition

then the model can be applied to organisational data bases to reveal any

inconsistencies in the allocation of overhead costs and thereby alert

management to these inconsistencies for further investigation. In addition

overhead cost adjustments for product deletions or product additions can

be established through the application of the model.

Traditional cost accounting systems simply apply the cost driver (e.g. direct

labour hours) to determine the level of overhead allocation to a new

product, whereas the deletion of a product without an offset in capacity

demand will distribute the allocated overheads from the deleted product to

all other products on a resource consumption basis. The underlying

6

Data bases were c reated with the aid of the random num ber generator function found in most spreads heet

application. The author used Corel Quattro Pro for the generation of the data bases.

132

assumption for such re-distribution of overhead costs is based on the

premise that demand and costs behave in a linear relationship. This

assumption is evidenced in most management accounting textbooks where

the determination of overhead predictions follows the application of

simplistic linear regression models (Horngren et al, 1994, 1996).

3.3 Data Base Generation and Pattern Recognition

The development of the model (7) required the analysis of a number of data

bases with varying numbers of elements and varying parameter

assumptions. During this process data bases with total element numbers

of 500, 1000, 2500 and 4000 were created randomly6 together with

parameters that represented product demand, price and shape factor. For

each of these populations 800 data bases were created. In addition, for

each random generated data base a model computed database was

produced to provide a comparison between the parallel bases. The final

number of generated data bases amounted to 6400 ( 800 for each 500 item

level, 1000 item level, 2500 item level and for the 4000 item level - and the

same number for each of these item numbers through the computed data

base). The metrics for price level was varied between $0.01 and $10.00

and between $0.01 and $100. Demand metrics were varied between 1 and

5000 and 1 and 10000 items.

133

The initial number of generated data bases using the “uniform” distribution

function produced consistent distributions at the(20/50) level. While this

outcome was of only minor concern to test the developed model it did not,

however, mirror the reported empirics (Koch, 1998). In order to generate

data bases that reflect the (20/80) distribution a shape factor was

introduced and varied at the upper ranges. The shape factor was randomly

varied between 1 and 1.4 in the first hundred data bases for each

population and between 1 and 1.45 for the second hundred data bases. For

all the items data bases the shape factor was held constant for changes in

price and demand. The permutations for each of the selected item data

bases were as follows:

Price range Demand range Shape factor

Data base 1 $0.01 - $10 1 - 5000 1 - 1.4Data base 2 $0.01 - $10 1 - 5000 1 - 1.45Data base 3 $0.01 - $10 1 - 10000 1 - 1.4Data base 4 $0.01 - $10 1 - 10000 1 - 1.45Data base 5 $0.01 - $100 1 - 5000 1 - 1.4Data base 6 $0.01 - $100 1 - 5000 1 - 1.45Data base 7 $0.01 - $100 1 - 10000 1 - 1.4Data base 8 $0.01 - $100 1 - 10000 1 - 1.45

All of the 3200 data bases were submitted to standard statistical analysis

(ANOVA) to determine within group and between group differences and were

found to be statistically similar as evidenced by the following tables (Table 3-1 -

Table 3-4). The model generated data bases produced similar non significant

results for differences between the “real” random data base and the parallel

7

The com plete data for all data bas e values are available from the author on request. As the main purpose of the

modelling process was the generation and testing of error free data bases, the inclusion of the s tatist ical analysis

of the model generated data bases are not relevant to this process.

134

model data base for the same 3200 data bases.7 However, each “real” data base

was submitted to a standard ANOVA test against its parallel “model” data base

to determine that the error term was within the level of insignificance. There was

no single case in which the F value exceeded the critical F value for each of the

3200 cases and it can therefore be stated with confidence that the model is

robust within the 95% confidence level that formed the basis for all ANOVA tests.

135

TABLE 3-1

Results of ANOVA for data distribution of 8 (500 items) data bases

Data 500 Price $ Demand # Shape F.(^2) ANOVA(Source of Variation) SS df M S F P-value F crit

1-10 1-5000 1-1.45 Between Groups 2.74 99 0.028 0.743 0.974 1.245

W ithin Groups 1857.47 49900 0.037

Total 1860.21 49999

1-10 1-5000 1-1.4 Between Groups 2.37 99 0.024 0.589 1.000 1.245

W ithin Groups 2029.29 49900 0.041

Total 2031.67 49999

1-10 1-10000 1-1.45 Between Groups 2.38 99 0.024 0.673 0.995 1.245

W ithin Groups 1780.57 49900 0.036

Total 1782.95 49999

1-10 1-10000 1-1.4 Between Groups 2.56 99 0.026 0.660 0.996 1.245

W ithin Groups 1956.84 49900 0.039

Total 1959.40 49999

1-100 1-5000 1-1.45 Between Groups 2.12 99 0.021 0.667 0.996 1.245

W ithin Groups 1598.44 49900 0.032

Total 1600.56 49999

1-100 1-5000 1-1.4 Between Groups 2.45 99 0.025 0.690 0.992 1.245

W ithin Groups 1788.47 49900 0.036

Total 1790.92 49999

1-100 1-10000 1-1.45 Between Groups 2.24 99 0.023 0.723 0.983 1.245

W ithin Groups 1560.17 49900 0.031

Total 1562.40 49999

1-100 1-10000 1-1.4 Between Groups 2.37 99 0.024 0.693 0.991 1.245

W ithin Groups 1725.98 49900 0.035

Total 1728.35 49999

136

TABLE 3-2



1-10 1-5000 1-1.45 Between Groups 2.93 99 0.030 0.806 0.922 1.245

W ithin Groups 3665.13 99900 0.037

Total 3668.06 99999

1-10 1-5000 1-1.4 Between Groups 2.91 99 0.029 0.730 0.980 1.245

W ithin Groups 4025.23 99900 0.040

Total 4028.14 99999

1-10 1-10000 1-1.45 Between Groups 1.82 99 0.018 0.516 1.000 1.245

W ithin Groups 3570.87 99900 0.036

Total 3572.69 99999

1-10 1-10000 1-1.4 Between Groups 2.91 99 0.029 0.761 0.963 1.245

W ithin Groups 3862.74 99900 0.039

Total 3865.65 99999

1-100 1-5000 1-1.45 Between Groups 2.91 99 0.029 0.916 0.712 1.245

W ithin Groups 3208.18 99900 0.032

Total 3211.09 99999

1-100 1-5000 1-1.4 Between Groups 2.79 99 0.028 0.796 0.933 1.245

W ithin Groups 3538.88 99900 0.035

Total 3541.68 99999

1-100 1-10000 1-1.45 Between Groups 1.74 99 0.018 0.561 1.000 1.245

W ithin Groups 3124.99 99900 0.031

Total 3126.72 99999

1-100 1-10000 1-1.4 Between Groups 2.77 99 0.028 0.818 0.906 1.245

W ithin Groups 3412.34 99900 0.034

Total 3415.10 99999

137

TABLE 3-3



1-10 1-5000 1-1.45 Between Groups 1.88 99 0.019 0.513 1.000 1.245

W ithin Groups 9261.28 249900 0.037

Total 9263.16 249999

1-10 1-5000 1-1.4 Between Groups 2.34 99 0.024 0.585 1.000 1.245

W ithin Groups 10083.78 249900 0.040

Total 10086.12 249999

1-10 1-10000 1-1.45 Between Groups 2.32 99 0.023 0.662 0.996 1.245

W ithin Groups 8835.62 249900 0.035

Total 8837.94 249999

1-10 1-10000 1-1.4 Between Groups 1.86 99 0.019 0.481 1.000 1.245

W ithin Groups 9730.35 249900 0.039

Total 9732.20 249999

1-100 1-5000 1-1.45 Between Groups 2.05 99 0.021 0.644 0.998 1.245

W ithin Groups 8027.21 249900 0.032

Total 8029.26 249999

1-100 1-5000 1-1.4 Between Groups 1.79 99 0.018 0.506 1.000 1.245

W ithin Groups 8916.52 249900 0.036

Total 8918.31 249999

1-100 1-10000 1-1.45 Between Groups 1.63 99 0.016 0.529 1.000 1.245

W ithin Groups 7785.79 249900 0.031

Total 7787.42 249999

1-100 1-10000 1-1.4 Between Groups 1.71 99 0.017 0.503 1.000 1.245

W ithin Groups 8602.38 249900 0.034

Total 8604.09 249999

138

TABLE 3-4



1-10 1-5000 1-1.45 Between Groups 1.93 99 0.019 0.527 1.000 1.245

W ithin Groups 14799.72 399900 0.037

Total 14801.65 399999

1-10 1-5000 1-1.4 Between Groups 2.42 99 0.024 0.660 0.996 1.245

W ithin Groups 14793.63 399900 0.037

Total 14796.04 399999

1-10 1-10000 1-1.45 Between Groups 2.63 99 0.027 0.747 0.972 1.245

W ithin Groups 14188.00 399900 0.035

Total 14190.62 399999

1-10 1-10000 1-1.4 Between Groups 2.53 99 0.026 0.658 0.997 1.245

W ithin Groups 15550.27 399900 0.039

Total 15552.80 399999

1-100 1-5000 1-1.45 Between Groups 1.78 99 0.018 0.557 1.000 1.245

W ithin Groups 12907.86 399900 0.032

Total 12909.64 399999

1-100 1-5000 1-1.4 Between Groups 1.86 99 0.019 0.526 1.000 1.245

W ithin Groups 14248.95 399900 0.036

Total 14250.81 399999

1-100 1-10000 1-1.45 Between Groups 1.74 99 0.018 0.565 1.000 1.245

W ithin Groups 12420.98 399900 0.031

Total 12422.72 399999

1-100 1-10000 1-1.4 Between Groups 1.82 99 0.018 0.534 1.000 1.245

W ithin Groups 13743.32 399900 0.034

Total 13745.14 399999

139

To reduce the limitation of subjectively choosing the 20% focal point of the

(x) dimension, a stratified selection of the random generated data bases

were used and additional focal points (x values) at the 10%, 30%, 40%,

50%, 60% and 70% level were submitted to analysis to determine

variations in error levels. The range of error terms at any of these levels

remained within the original range (refer Table 3.5) at the 20% level. This

analysis clearly established the validity and robustness of the model and

justified the subjective choice of the 20% level as it is representative of the

20/80 rule discussed in other literature (Koch, 1998). A further comment on

the use of a model that mirrors the original data base is its variation at the

point estimates. These point estimates are useful to establish domain

pattern similarities and also provide the basis for comparison between

original data base and model generated data base. However, this function

is limited to verify the integrity of an existing data base and identify the level

of variation for further detailed investigation. A more important function of

the model however, is the ability to compute item contributions within the

cumulative framework. For this reason it is important to analyse and

compare the differences in item contribution rather then the item’s point

estimate.

Point estimates compare the cumulative percentage between “real” and

model data base values which, given the argument provided earlier as to

140

the likelihood and risk of data base inaccuracy due to error entry and data

omission would render such comparison as meaningless and therefore the

associated error term would not be indicative of the robustness of the

model. Table 3-5 shows the analysis of this pairwise comparison for each

of the 3200 data bases with average, maximun and minimum values for

both the incremental and point estimate values.

Error term analysis is absolutely necessary to establish the robustness of

the model under varying parameters and to calculate an upper and lower

boundary that can be applied to predictive data. For each of the random

generated data bases the standard statistical parameters for populations

(mean, variance and standard deviation) were recorded to establish the

range of values over the 3200 data bases used in the modeling process.

The standard notation for the mean, variance and standard deviation can

be found in any introductory statistics text but is shown below for

completeness.

Mean

Variance

Standard Deviation

141

Table 3.5 shows the values of these parameters. Here the argument could

be advanced that the maximum and minimum values from the 3200 data

bases are a better indication of the confidence interval limits than the

calculation of the confidence interval at the 95% level. However, for

completeness and accepted practice the confidence interval for the data

presented in Table 3-5 is computed as:

Table 3.5

Error data for incremental and point differences

INCREMENTPOINT

µ F2F µ F2

F

-0.00001% 0.00002% 0.04203% Mean-N 500 -0.42661% 0.00863% 0.83094%

-0.02074% 0.00006% 0.06036% Mean-N 1000 -0.40267% 0.00964% 0.87698%

0.00001% 0.00000% 0.00653% Mean-N 2500 -0.40291% 0.01586% 1.10361%

-0.00004% 0.00000% 0.00395% Mean-N 4000 -0.40267% 0.00831% 0.87421%

-0.00000% 0.00017% 0.13131% Max-N 500 0.09425% 0.03186% 1.78503%

-0.00042% 0.00038% 0.19420% Max-N 1000 0.02365% 0.08939% 2.98974%

0.00021% 0.00000% 0.01494% Max-N 2500 -0.03714% 0.12288% 3.50549%

-0.00000% 0.00000% 0.00900% Max-N 4000 -0.01889% 0.02293% 1.51419%

-0.00003% 0.00000% 0.01540% Min-N 500 -1.29750% 0.00045% 0.21124%

-0.07956% 0.00000% 0.00893% Min-N 1000 -1.01633% 0.00044% 0.21089%

-0.00029% 0.00000% 0.00266% Min-N 2500 -0.83952% 0.00034% 0.18461%

-0.00040% 0.00000% 0.00124% Min-N 4000 -0.76804% 0.00025% 0.15828%

Note: Subscripts D and M identify “real” data base and generated model data base item values.

The confidence interval for the incremental data with a maximum F (refer

Table 3.5) = .1942%(±1.96) = ±.380632% and maximum : (refer Table 3.5)

142

= .00021%x(±.380632%) thereby creates a confidence interval with a lower

boundary of -.3804 and an upper boundary of +.3808. While the point

estimate has little relevance for the computation of predictive data (e.g.

overhead) it shows a substantially greater confidence interval then the

incremental error term. For completeness and using the same values as for

the incremental value the point estimate interval is for the maximum F (refer

Table 3.5) = 3.505%(±1.96) = ±6.87% and a maximum : (refer Table 3.5)

= .0904%x(±6.87%) = -6.78% and +6.96%.

The general shape of one of those (2500 element population) random

created data bases together with its computed model (7) values are shown

in Figure 3-1.

FIGURE 3-1

Data Base and Model Comparison

143

Figure 3-2 illustrates the error distribution of the data comparison for

differences between the individual increment at each point estimate. The

error distribution illustrated in Figure 3-2 shows an overall distribution range

from + .067% to -.051% which is atypical for most of the compared data

bases.

FIGURE 3-2

Typical Incremental Error Distribution

While this error distribution shows a minimal amount of variation at each of

the incremental point estimates, it does not reveal the variation or standard

deviation of the error term to construct a meaningful confidence interval.

W e are assisted by a standard summary measure for population data sets

and do not have to rely on estimates of the main parameters of interest.

144

Having established the basic parameters for the population it is now

possible to construct appropriate confidence intervals. It is often desirable

to first decide on a confidence coefficient that allows the construction of the

range of the confidence interval. The confidence coefficient is commonly

expressed as a percentage and having decided in the earlier ANOVA

computations to use an alpha level (") of .05 it is consistent with this level

to establish a confidence coefficient of .95 or 95%.

Such interval determines that the calculated point estimate of a population

will have an upper and lower limit and that the calculated value will, with a

95% confidence level, be an accurate prediction of the value computed.

The parameters for the random generated database represented in Figure

3-1, 3-2 and 3-3 have been computed to have a mean of the incremental

value differences of 0.00, a variance of 0.000 and a standard deviation of

0.0001%. These values would construct a confidence interval which at the

95% as well as the 99% confidence coefficient becomes equal to the point

estimate at the predicted value. A more probing test would have to

consider the differences in point values between the random generated

data base and the model computed values. This error distribution is

presented in Figure 3-3 and shows a more discernable error distribution,

the values calculated for the error distribution shown in Figure 3-3 are as

145

follows: mean = -.379378%, variance = .00358% and the standard

deviation = .598%. We are now able to construct a confidence interval for

the illustrated data base. At the 95% confidence coefficient a (z) value of

1.96 is taken from a standard table for cumulative probabilities of a

standard normal distribution. This will establish a confidence interval of

±(.598)*1.96 = 1.172% and therefore an upper and lower limit for the

random generated data base ranging from -1.551% to .793%.

FIGURE 3-3

Error Distribution of Point Estimates

To extend the example it is now possible to use an organisation’s total

overhead costs and allocate individual product overhead costs an the basis

of the product’s ranking in the forecasted data base.

146

Product No:53321 is ranked 150 in the projected data base. The

parameters for the interval estimate, employing the model developed in (7)

are c = 6.28135, d = .50205 and the denominator value is 125.48659.

Given these values computes an incremental percentage for item 150 of

.1726%. The organisation projected a total overhead cost on the

assumption that underlie the forecasted product data of 2.6 million dollars.

Product 53321 has been given a demand forecast of 750 units. The

allocated overhead cost per unit would therefore be (2.6 * 106 *

.001726)/750 = 5.98 with an confidence interval of -1.55% to .793% or from

$5.90 to $6.03.

While the confidence interval will vary from data base to data base,

however, generalised limits can be expected to be within the range of -

2.2% to + 1.3% on the averages computed across the random generated

data bases. It is therefore suggested that data base integrity as far as

recording and omission errors are concerned should fall within these

generalised limits and that data base modelling that produces error terms

outside these limits should be investigated for data errors both at data entry

level and omission levels.

Although the arguments advanced in the previous section have established

with reasonable certainty that variations in price, demand and distribution

147

pattern (shape factor) consistently show no differences between each of

800 database within the common item domain, what has not been tested

are the relationships of data bases within the same domain (demand and

shape factor) but with varying items. The statistical results shown in Tables

3-1 to 3-4 have only supported the hypothesis that data base differences

do not exist when price, demand and shape factor variables are randomly

changed. These changes are presumed to be equivalent to changes in

organisational budgetary cycles.

Such situation would be typical in most organisational situations as both

pricing policies and product portfolio compositions are subject to strategic

consideration. It is therefore of interest to test the relationship of item

changes within a given domain to ascertain if these relationships will also

provide a statistical insignificant difference. This proposition is of particular

value in determining the integrity of an organisational data base to analyse

any inconsistencies in domain values that are due to recording errors. As

each of the “real” data bases were generated by a computer based random

generator that changed the various parameters, the resulting data bases,

by implication, are free from any entry or omission error and therefore

provide a benchmark test for the determination of data inconsistencies

within a given domain. This assumption is only valid if the statistical

analysis supports this proposition.

148

Table 3-6 shows the results of the ANOVA tests for a random data base

sample selection of five (5) data bases from each of the “real” data bases

with varying parameters for price, demand and shape factor and drawn

from each 500, 1000, 2500, and 4000 item data base. Again, the ANOVA

results clearly support the earlier advanced proposition of domain

consistency, thereby providing a basis for predicting data base integrity.

Results that do not support the null hypothesis of equivalent mean values

between either period data or between data base and computed model

values should trigger investigations as to error existence in the

organisational data bases.

As none of the tested data bases revealed any significant results as

evidenced by the F values it was not necessary to conduct any post hoc

test to determine which combinations of data base within a selected domain

causes a level of significance. Therefore, it was not necessary to apply

either the Bonferroni or the Tukey range tests to the data.

149

TABLE 3-6

Results of ANOVA for data distribution of 5 random selected data bases

from the 500, 1000, 2500 and 4000 items data bases with varied

parameters for price, demand and shape factor.

Price $ Demand # Shape F.(^2) Source of Variation SS df M S F P-value F crit

Data 500 1-10 1-5000 1-1.45 Between Groups 0.499 19 0.026 0.711 0.811 1.587

Data 1000 W ithin Groups 1475.942 39980 0.037

Data 2500

Data 4000 Total 1476.441 39999



Data 2500

Data 4000 Total 1278.176 39999




Data 2500

Data 4000 Total 1551.334 39999



Data 2500

Data 4000 Total 1418.735 39999




Data 2500

Data 4000 Total 1418.239 39999



Data 2500

Data 4000 Total 1232.378 39999




Data 2500

Data 4000 Total 1556.816 39999



Data 2500

Data 4000 Total 1371.298 39999

150

3.4 Chapter Summary

Although the previous discussion has established that data base domains

remain similar over time and error terms are within narrow boundaries, it

requires additional data base analysis to confirm the generalisability of the

model’s prediction ability as to error detection.

In the next chapter a number of organisational data bases are analysed for

both domain consistency and data element accuracy.

151

4. CASE STUDY ANALYSIS

4.1 Introduction

In the previous chapter a model for the identification of domain consistency

and data base accuracy was developed and extensively tested against

random number generated (real) data bases with different parameters. The

resultant statistical analysis to test the robustness of the developed model

clearly demonstrated its validity under varying parameter choices. The

application of the model to test actual data bases should reveal that these

data bases are either indifferent, as to their data accuracy, or at worst do

not confirm domain consistency between different periods under review.

Furthermore, actual data bases must be represented by census or

population data over a number of periods and thereby enhance the value

and applicability when compared with survey data (representing samples

rather than populations). A choice of three divergent data bases

(representing census data) to analyse domain consistency and data

accuracy have been selected on the basis of their anecdotal preconception.

Stock Exchange daily security transaction data by its sensitive nature

should reveal both domain consistency and data base integrity. As such

data is readily available from a number of public sites, data accumulation

and analysis are relative easy tasks. Furthermore, daily share trading

transaction records have similar characteristics to organisational inventory

152

records as a number of securities are not traded every day whereas others

are traded on a daily basis but with different volumes. These daily changes

can be associated with an organisation’s inventory records where annual

product changes may experience similar patterns.

A second data base that also presents a data base item change on an

annual basis is university student enrolment records. The number of

students enrolled in different programs and subjects from year to year

differs as well as new programs being offered while some of the less

supportable programs may either be abandoned or combined with other

more viable programs. As the majority of Australian universities are public-

funded institutions, a biannual consolidation of student enrolment data by

government funding agencies becomes a prerequisite condition for funds

distribution. Since its restructured funding formula in the early 1990s none

of the 39 publicly funded universities ever reported a reduction in student

enrolment data according to comments offered by financial staff of the

Department of Education, Science and Training (DEST). Such anecdotal

evidence would suggest that student enrolment data is well managed by

university administrators but is likely to contain both domain as well as data

item inaccuracies that should be detectable through the application of the

model developed in the previous chapter.

153

The third of the data bases analysed by the developed model comes from

the inventory records of an Australian subsidiary of a multinational

company. The data was taken from existing company records for the period

from 1993 to 1998. Although the recorded period comprises six years only,

three years were selected for data analysis as the data inaccuracies in the

other three years were identified by company officers but remained

uncorrected. The company intended to restructure and consolidate a

number of product-based data bases to reduce the recognised data

inaccuracy between individual data bases established for different

functional responsibilities. While production-based data was recorded for

the purpose of product manufacture scheduling, inventory records were

based on actual sales with substantial item detail differences between

these data bases. In addition the company employed a rather unusual

overhead allocation system by combining raw materials and some direct

labour hours as basis for overhead allocations to individual products. The

cost-pool for determining overhead costs was also inconsistent with

accumulating some product related direct labour hours as well as more

traditional indirect costs. While total product costs appeared to represent

a realistic cost level, a number of product items varied substantially from

one period to the next without evidence in production process or raw

material changes. This data base is used to not only test the data base

8

http: //www.intersuisse.com.au/shareprices2_frames.htm, data from this source was downloaded on a daily basis.

The data contains only those s hares that were traded during the day and not the com plete listing. T he number of

shares traded during the 14 day period ranged from 723 to 761. Investigation of each of the daily records revealed

a number of securities were listed but had no transaction rec ords . W hen the com pany that produces these records

was contacted it was explained that transactions are listed in m ultiples of 1000 and that the listed securities w ith

0 transaction entries may have been trading in less than marketable parcels.

154

integrity and accuracy but applies the model generated values to assign

overhead costs to individual products.

The Stock Exchange and University data, although selected from different

sectors of the Economy representing service industries, display similar

characteristics to the manufacturing industry inventory data base

characteristics over a number of periods. The model can, therefore, also be

applied to these industries for the allocation of discretionary costs

(overhead costs) to selected activity centres.

4.2 Case Study Analysis Stock Exchange Data.

A readily accessible data base that displays similar characteristics to

inventory movements in organisations is the daily share trading

transactions of major stock exchanges. Share trading data (share

transactions by volume and value from the Sydney Stock Exchange,

Australia8) over a period of seven days (August 31 to September 10) were

evaluated to determine if pattern similarity does exist. While the daily share

trading deals with a large number of transactions in the same securities are

considerable, there are a discernable number of shares that are unique to

155

a day’s trading pattern. In addition, changes in the number of specific

securities together with their price fluctuations mirror product characteristics

of demand and competition induced price adjustments. Table 4-1 shows the

results of the ANOVA-test together with the critical values at the 20% share

number level for each of the (7) days.

Table 4-1,

Results of ANOVA for Australian Share data("=.05)Source of

Variation

SS df M S F P-value F crit

Between Groups 0.093 6 0.015 0.601 0.730 2.100

W ithin Groups 132.419 5159 0.026

Total 132.512 5165

Day 1 2 3 4 5 6 7

at 20% (x) 83.24% 84.72% 83.54% 84.33% 84.90% 85.10% 83.63%

As the F value is well within the critical limit, the seven day data clearly

demonstrates domain consistency (data base integrity) which is expected

from such data base. Domain consistency refers to data from different

periods displaying similar pattern consistency and therefore must be judged

to come from the same organisation.

Table 4-2,

F-test for daily transactions/model values("=.05)

Date

Parameter

Aug

31

Sept

2

Sept

3

Sept

6

Sept

7

Sept

8

Sept

13

F 1.490 1.170 1.122 1.054 1.069 1.080 1.430

P-value 0.000 0.015 0.059 0.238 0.181 0.127 0.000

F-crit. 1.128 1.127 1.128 1.130 1.129 1.130 1.128

N 746 761 747 728 739 723 748

156

However, when the transaction data for each of the seven days is

compared with the model generated values and for three of the seven days

(Aug. 31, Sept 2 and Sept 13) the results indicate statistical significance as

shown in Table 4-2. Such indication suggests data base inaccuracy. On

contacting the organisation that compiles the stock exchange transaction

data it was revealed that inaccuracies are possible as some of the traded

securities are traded in non marketable parcels and that aggregation for

data base inclusion may lead to recorded inaccuracies. It was further

revealed that it is possible to omit some of the traded shares due to delays

in private broker recording of transactions.

4.3 Case Study Analysis University Enrolment Data

Although the previous case study example demonstrates the inherent

hazard in using existing data base data for future predictions of component

characteristics and behaviour, another type of data base that requires

accuracy but maybe open to unchecked acceptance by funding authorities

can be found in the Australian higher education sector. The Australian

higher education sector is dominated by government funded public

universities. W ith such a funding structure it is necessary to submit

semester-based student enrolment data to a central authority for

substantiating the allocated funds from public sources. The Department of

Education, Science and Training [DEST] is the collector of such data on a

9

The data collection by DEST is based on two cut-off dates(31st of March-Autumn semester and 31s t of August-

Spring sem ester) f or each of the semes ters and requ ires universities to subm it their actual student enrolment data

for each of the sub jec ts of fered by the university. As there is a substantial var iety in student records systems

accross the Aus tralian univers ity sec tor it is not uncommon that the reported student enrolments at the cut-off dates

vary from the actual classroom numbers.

10

T his was confirmed by a DEST officer in an telephone interview conducted on the 22-5-2002. The amou nt is

approximately equivalent to the Higher Education Contribution Component [HECS] but in any case A$ 2,600 per

EFTSU .

157

biannual basis9 to maintain accurate records for statistical analysis and

justification for funding. However, individual university funding is based on

a student/program profile that estimates the number of enrolments in

equivalent full time students units (EFTSU) established in 1990 and

provides marginal funding10 for reported over enrolled students. As under

enrolment is penalised with a deduction from operating funding allocations

equivalent to the marginal funding amount it is unusual for universities to

report under enrolments. It is more common for universities to report over

enrolments to at least attract the marginal funding allocation. DEST does

conduct internal audits to reconcile reported data with profile data but has

only limited opportunities to check the reported data accuracy submitted by

universities.

As each university is required to submit their data in subject and student

enrolment groupings it is of interest to check a random sample of university

data bases to ascertain both domain consistency and data base integrity by

applying and statistically comparing the model computed values with those

of the actual data records. DEST supplied the data for 12 universities that

11

The data for University 13 was supplied by the University and not from DEST. As the author ask f or the most recent

5 year data the period analysed started in 1998 and not in 1996 as for the res t of the university data.

158

included the largest university from each of the six States of Australia and

a further six randomly selected universities one from each of the States.

Also included was one additional university that supplied its data directly

to make the total sample 13 (32%) from a total of 41 public sector

universities. Tables 4-3 to 4-17 show the results of the ANOVA analysis for

each of the 13 universities in the sample over a 6-year period from 1996 to

2001.

TABLE 4-311 (University 13)

Results of ANOVA for 5 year DEST data ("=.05)

SOURCE OF VARIATION SS df MS F P-value F-c rit

Between Groups 0.0888 1.0000 0.0888 2.4595 0.1169 3.8435

W ithin Groups 161.1088 4464.0000 0.0361

Total 161.1975 4465.0000

YEAR DES T1998 DES T1999 DES T2000 DES T2001 DES T2002

at 20% (x) 0.7375 0.7437 0.7482 0.7564 0.7333


F-test for yearly enrolment records/model values (("=.05)

YEAR

PARAMETER

DEST1998 DEST1999 DEST2000 DEST2001 DEST2002

F 2.460 2.466 2.697 2.481 1.980

P-value 0.117 0.116 0.101 0.115 0.159

F-crit. 3.844 3.844 3.844 3.844 3.844

N 2233 2242 2210 2236 2146

Table 4-3 clearly indicates that the enrolment data for University 13 is

consistent and the data analysis supports that it comes from the same

domain. Table 4-4 also supports the analysis that each year’s enrolment

159

data when compared with model generated values shows no statistical

significant differences as each of the p-values is clearly above the level of

significance ("=.05). The values for each of the 12 Universities that was

supplied by the (DEST) database are shown in tables 4-5 to 4-17.

160

Table 4-5ANOVA FOR EACH OF THE 12 UNIVERSITIES’ 5 YEAR STUDENTS ENROLMENT RECORDS

University Source of Variation SS df MS F P-value F crit

Between Groups 0.1549 5 0.0309 0.7502 0.5858 2.2147

Within Groups 550.1011 13319 0.0413

1 Total 550.2560 13324

Year DEST1996 DEST1997 DEST1998 DEST1999 DEST2000 DEST2001

at 20%(x) 70 71.55% 71 70 72.42% 73

Between Groups 0.2524 5 0.0504 1.1042 0.3556 2.2149

Within Groups 503.9953 11023 0.0457

2 Total 504.2477 11028


at 20%(x) 66 67.71% 69.03% 70.11% 69.18% 69.45%

Between Groups 1.5615 5 0.3123 8.0096 0 2.2145

Within Groups 859.0447 22031 0.0389

3 Total 860.6063 22036


at 20%(x) 66 68.01% 69.05% 68.78% 71.12% 72.22%

Between Groups 1.5315 5 0.3063 5.2622 0 2.2174

Within Groups 157.5125 2706 0.0582

4 Total 159.0440 2711


at 20%(x) 52.41% 48.94% 54.34% 58.01% 62.31% 60

Between Groups 0.9111 5 0.1822 4.5303 0.0004 2.2148

Within Groups 503.8771 12527 0.0402

5 Total 504.7882 12532


at 20%(x) 64.87% 67.14% 68.76% 69.44% 70.55% 69.11%

Between Groups 0.2785 5 0.0557 1.3173 0.2533 2.2147

Within Groups 590.8926 13974 0.0422

6 Total 591.1711 13979


at 20%(x) 68 67.47% 69.32% 70.51% 70.83% 69.11%

Between Groups 0.1947 5 0.0389 0.8668 0.5023 2.2147

Within Groups 575.1384 12802 0.0449

7 Total 575.3331 12807


at 20%(x) 68.35% 68.60% 68.88% 70.17% 69.65% 70.80%

Between Groups 1.0274 5 0.2054 5.3321 0 2.2144

Within Groups 929.8271 24127 0.0385

8 Total 930.8546 24132


at 20%(x) 71.15% 71.31% 72.19% 73.39% 74.03% 75.35%

Between Groups 2.8003 5 0.56 14.5976 0 2.2145

Within Groups 712.5457 18572 0.0383

9 Total 715.346 18577


at 20%(x) 67.32% 70.17% 72.04% 73.76% 74.92% 74.50%

Between Groups 1.4498 5 0.2899 6.3894 0 2.2145

Within Groups 967.3126 21314 0.0453

10 Total 968.7625 21319


at 20%(x) 73.48% 69.66% 68.24% 69.30% 70.27% 69.00%

Between Groups 0.2805 5 0.0561 1.375 0.2301 2.2143

Within Groups 1211.8667 29697 0.0408

11 Total 1212.1473 29702


at 20%(x) 70.37% 70.81% 70.34% 69.21% 68.35% 69.18%

Between Groups 0.2131 5 0.0426 1.0784 0.3699 2.2143

Within Groups 1436.3967 36345 0.0395

12 Total 1436.6098 36345


at 20%(x) 74.12% 73.61% 73.04% 73.05% 73.96% 74.73%

161



Year

Parameter 1996 1997 1998 1999 2000 2001

F 5.2958 18.8685 5.7304 6.3930 3.9600 2.3856

P - VALUE 0.0214 0.0000 0.0167 0.0115 0.0467 0.1225

F - CRIT. 3.8438 3.8437 3.8435 3.8435 3.8435 3.8434

N 2001 2105 2275 2240 2323 2381



Year

Parameter 1996 1997 1998 1999 2000 2001

F 2.6570 5.7171 1.6908 2.8266 3.9600 4.7954

P - VALUE 0.1032 0.0169 0.1936 0.0928 0.0467 0.0286

F - CRIT. 3.8440 3.8440 3.8435 3.8439 3.8435 3.8441

N 1848 1848 1881 1894 1777 1781



Year

Parameter1996 1997 1998 1999 2000 2001

F 17.4541 9.2823 17.5918 18.6614 16.2156 13.7161

P - VALUE 0.0000 0.0023 0.0000 0.0000 0.0001 0.0002

F - CRIT. 3.8428 3.8428 3.8427 3.8427 3.8427 3.8427

N 3384 3603 3622 3688 3893 3847



Year

Parameter1996 1997 1998 1999 2000 2001

F 0.1250 2.1144 1.9067 2.6233 1.2642 4.2729

P - VALUE 0.7238 0.1463 0.1677 0.1057 0.2611 0.0390

F - CRIT. 3.8565 3.8524 3.8525 3.8518 3.8499 3.8499

N 311 425 424 452 550 550

162



Year

Parameter1996 1997 1998 1999 2000 2001

F 2.9889 8.7720 7.3065 5.4047 4.8786 6.1005

P - VALUE 0.0839 0.0031 0.0069 0.0201 0.0272 0.0136

F - CRIT. 3.8437 3.8437 3.8436 3.8437 3.8437 3.8437

N 2047 2119 2133 2091 2079 2064



Year

Parameter1996 1997 1998 1999 2000 2001

F 9.0725 7.8033 6.5787 5.6026 3.3271 6.1005

P - VALUE 0.0026 0.0052 0.0104 0.0180 0.0682 0.0136

F - CRIT. 3.8434 3.8434 3.8434 3.8434 3.8435 3.8437

N 2437 2369 2395 2415 2300 2064



Year

Parameter1996 1997 1998 1999 2000 2001

F 6.3623 5.1477 4.8363 5.6937 5.0848 3.5848

P - VALUE 0.0117 0.0233 0.0279 0.0171 0.0242 0.0584

F - CRIT. 3.8436 3.8436 3.8436 3.8436 3.8437 3.8437

N 2208 2161 2136 2167 2065 2070



Year

Parameter1996 1997 1998 1999 2000 2001

F 16.5135 15.9756 15.8090 11.7635 11.0798 32.9104

P - VALUE 0.0000 0.0001 0.0001 0.0006 0.0009 0.0000

F - CRIT. 3.8426 3.8426 3.8426 3.8426 3.8426 3.8427

N 3975 4097 4112 4045 4054 3850

163



Year

Parameter1996 1997 1998 1999 2000 2001

F 19.4158 13.4952 8.9257 7.1486 6.1205 7.5652

P - VALUE 0.0000 0.0002 0.0028 0.0075 0.0134 0.0060

F - CRIT. 3.8427 3.8428 3.8430 3.8431 3.8431 3.8431

N 3605 3359 3087 2882 2886 2759



Year

Parameter1996 1997 1998 1999 2000 2001

F 5.8657 8.0663 7.7396 6.2316 6.9143 10.1128

P - VALUE 0.0155 0.0045 0.0054 0.0126 0.0086 0.0015

F - CRIT. 3.8428 3.8429 3.8429 3.8428 3.8427 3.8426

N 3533 3190 3207 3504 3819 4064



Year

Parameter1996 1997 1998 1999 2000 2001

F 7.8837 14.2321 14.8194 18.4598 18.0419 16.7161

P - VALUE 0.0050 0.0002 0.0001 0.0000 0.0000 0.0000

F - CRIT. 3.8423 3.8423 3.8424 3.8424 3.8425 3.8425

N 5454 5389 5112 4790 4503 4455



Year

Parameter1996 1997 1998 1999 2000 2001

F 8.4186 9.4605 13.4837 12.2944 9.1065 7.8838

P - VALUE 0.0037 0.0021 0.0002 0.0005 0.0026 0.0050

F - CRIT. 3.8423 3.8423 3.8422 3.8422 3.8422 3.8422

N 5595 5810 6368 6211 6200 6167

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Of the 13 universities investigated for student data record integrity only one

passed the ANOVA test for both domain integrity and annual student

enrolment data accuracy. Of the remaining 12 universities one other could

be identified for domain integrity and student enrolment data accuracy for

three of the 6-year recording period. University 4s results are unusual in

that it does not indicate domain integrity but shows student enrolment data

accuracy for five of the 6-year recording period. All other universities show

statistically significant differences in student enrolment data records while

only seven of the 13 universities indicate domain integrity. W hile the

statistical analysis cannot determine the direction of the student enrolment

data inaccuracy, by implication it would appear that most of the

inaccuracies are skewed toward the over reporting rather than under

reporting. This assumption can be supported by the comment provided by

a DEST financial officer in stating that she was unaware of any under

reporting by universities since the establishment of the original university’s

profile. The suggestion here is that most university administrations are

more likely to over report as such strategy provides additional marginal

funding rather than a reduction in funding through under reporting student

enrolments.

An example may clarify the strategy pursued by universities. University (A)

has an enrolment profile established by DEST in 1991 of 12,000 for its then

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existing program structure. Additional approved programs will attract

additional government funding as the expected student enrolments are

expected to increase to a figure of 12,000 plus X. As university

administrators are familiar with the DEST profile for their university,

changes in student enrolment trends are projected as increasing at a

positive rate. Competition for students amongst universities, especially in

geographical areas were more then one university is accessible by

prospective students, may lead to negative trending of student enrolments

and therefore to reduced funding. Given the competition for public

education funding university administrators are reluctant to report negative

trending enrolment data.

It is, therefore, suggested that university administrators who are familiar

with the established profile for their university would try to match their

enrolment data with profile expectations rather than the accurate enrolment

data at the predetermined cut-off dates. Although, university administrators

are responsible for the reporting of enrolment data, such data is often

provided by academics in charge of subjects. In some cases there may

also be an incentive by academics responsible for subject administration

to report student numbers in excess of actual enrolments to maintain

marginal subject funding and to maintain subject viability.

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DEST has only limited resources to detect reported enrolment data

inaccuracies and relies on profile projected comparisons for questioning

data supplied by universities. Given the number of competing interests that

are involved in the recording of student enrolment data it is difficult for

funding authorities to provide the necessary incentives to universities to

establish internal record keeping systems that portray a more accurate

reflection of the actual student enrolments.

In summary, it has been demonstrated that the accuracy of recorded data

is questionable. Reasons for inaccurate data recording are multi faceted

and range from entry and omission errors (stock exchange data) to data

manipulations to reflect desired outcomes (university student enrolment

data).

4.3 Case Study Analysis Inventory Data

While there is limited empirical evidence as to unbalanced distribution

patterns within organisational inventory data bases from one period to

another, using the (3) year inventory record of the case data tends to

support the proposition that a firm’s inventory data base distribution shows

no significant variation. Evaluation of product data on the basis of cost

reduces the bias of revenue analysis caused by varying profit margins.

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Although the company’s records revealed a substantial product mix change

over the four-year review period, the distribution of overhead costs

remained statistically stable (refer to Table 4-18). The overhead cost

distribution follows a Pareto distribution with values at the 20% product

level of 76.73%, 77.81% and 77.03% (refer to Table 4-19) for the periods

1994-1997. Applying ANOVA analysis to test for the distribution

consistency over the four-year period confirmed that inventory distribution

patterns remain consistent. This finding provides further evidence that data

distributions within a domain remain fairly constant over time. The

closeness of these values at the critical 20% level is supported by the

analysis exhibited in Table 4-18. A further test for variance and population

means similarity must be applied to the yearly data when compared to the

model values. The standard F-test has been adopted for this analysis and

is shown in Table 4-18a for each of the three years that formed part of the

analysis.

Table 4-18, Table 4-18a,

Results of ANOVA for Inventory data("=.05) F-test for Model/Inventory("=.05)

Source of Variation SS df MS F P-value F-c rit

Parameters 1994 1996 1997

Between Groups 0.113 2 0.057 1.913 0.148 2.997 F 1.001 1.126 1.005

W ithin Groups 154.686 5223 0.030 P-value 0.499 0.007 0.461

Total 154.799 5225 F-cr it 1.063 1.063 1.083

The question that arises from the excessive variations between the “real”

data records and the mirrored generated model values, is, the applicability

of the model. The lack of theoretical research on explaining and supporting

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the Pareto rule as a law based on scientific replication consistency reduces

the generalisability of the presented case study data base analysis. The

application of the model was based on a subjective choice of a focal point

(the choice of the 20% (x) dimension) to mirror the existing unbalanced data

item distribution. While the initial data pair (0%/0%) and the terminal pair

(100%/100%)is not in dispute and fixed, it is the choice of focal data pair

that can invoke critical commentary as to the validity of the model’s

application.

To reduce this perceived subjectivity of focal point choice, a selection of

different focal points ranging from 10% to 70% (of x values) in 10%

intervals may produce the desired consistency of model applicability.

From the table it is noted that the results for 1994 and 1997 are not

significant indicating that the inventory distribution pattern is not statistically

different from the model values. The 1996 results, however, reveal a

significant deviation and on investigation it was found that the inventory

records for that year were incomplete and not adjusted for mistakes in data

recording. Adjustments to the data base would be accomplished at some

future period by company officers. Although statistically the results revealed

a notable inconsistency between the company’s data base and the model

generated values it did, however, confirm that the inconsistency was

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attributable to indifferent data capture rather than a loss of model

robustness.

Table 4-19

Model parameters for Case study data

Total O/H Cos ts $2,215,376.00 $2,289,604 $1,885,286

Year 1994 1996 1997

n 1742 1792 1932

Criteria DLH MAT. O/Head DLH* MAT. O/Head DLH MAT. O/Head

20%(x) 76.69% 86.75% 76.73% 86.45% 77.81% 76.70% 88.54% 77.03%

Rank (1) 2.22% 4.32% 2.22% 4.49% 4.02% 1.92% 5.09% 1.88%

c 7.116 9.149 7.111 9.3162 9.3787 6.9678 9.9268 6.9474

d .2668 .2443 .2678 .2299 .1618 .281 .2226 0.2883

17.0471 5.281 17.223 4.2158 1.5267 22.72 3.114 24.2259

Model Com parison (ANOVA analysis)

F-tes t ("=.05) 2.246 .8698 1.4405 .2829 3.5035 5.677 .135 4.677

F-c ritical 3.844 3.844 3.844 3.844 3.844 3.844 3.844 3.844

P value .134 .351 .2301 .5948 .0613 .0172 .713 0.0306

* data for d irect labour was incom plete and rec ords were not available to reconstruct the production data.

In Table 4-19 the computed model parameters for the three years under

review are shown. The values were computed with the aid of a standard

spreadsheet optimisation function and are based on the ranking of actual

direct labour hours, direct materials and overhead allocations. Although it

was demonstrated earlier (refer to Table 2-6) that the relationship between

direct labour hours and overhead costs under both traditional and ABC

based overhead distributions have a high correlation (r= .92 and .94

respectively) and therefore can be considered as a good proxy for model

parameter computation and comparison, the current case study data

revealed substantial inconsistencies in data recording and rendered direct

labour hours an unreliable proxy for purposes of comparison.

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Table 4-20 presents the results of the data comparison for three randomly

selected items from the inventory records for each of the three years under

review. The ranking column in Table 4-20 is based on the rank of the

selected items within the direct material sorted data base. Three randomly

selected items one from each of the high, medium and low volume

production was selected for comparison and substantial variations between

the actual overhead and the computed overhead values were identified.

When these variations were discussed with the production manager of the

company, it became evident that the internal records had not been

maintained properly and overhead allocations were based on material and

labour combinations that explained the inconsistency of the data. Further

interviews with the management accountant revealed that the company

maintained separate data bases for production control and inventory

records and a consolidation and between these data bases was not part of

the internal control system structure. The company is introducing a new

software package and hopes that the detected inconsistencies in overhead

allocations will be resolved through the application of the package which

provides the opportunity of data base consolidation and record comparison.

However, what has been demonstrated by the inventory record analysis is

the model’s ability to rank a related variable (direct material) and apply the

item percentage contribution to the computation of overhead allocations

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rather than relying on direct labour hours as a ranking base for such

computed allocations. The use of direct material as a ranking variable

provides the additional benefit of a clearer audit trail to establish objectivity

of data rather than the direct labour hour data if it is reliant on recorded

rather than standard costing compilations. What is, however, of interest is

the substantial variation in recorded as compared to computed costs and

would suggest that the inherent inconsistencies in overhead allocations

should not be attributed to the technique of applying single volume based

cost drivers (absorption costing) but rather the indifference of the prevailing

data recording system.

In chapter 3 it was established that the expected confidence limit between

“real” and model computed values at the 95% confidence level has an

upper and lower limit of -2.2% and +1.3% it is, therefore, possible to apply

this confidence interval to the data in Table 4-20 to determine the

magnitude of error that is present in the inventory data base.

TABLE 4-20

Cost Allocation Variances (Actual v Confidence Limits)

Product Year Demand Rank Ac tual Costs Model Cos ts Con f. Interval Variance

Material Total Un it Total Unit low high under over

1994 8149 12 $37,001 $4.54 $27,913 $3.42 $ 3.35 $ 3.46 31.20%

13801 1996 11333 6 $57,472 $5.07 $49,684 $4.38 $ 4.28 $ 4.44 14.20%

1997 1538 94 $6,492 $4.22 $3,959 $2.57 $ 2.51 $ 2.60 62.30%

1994 2 1732 $50 $25.00 $47 $23.26 $ 22.74 $ 23.56 6.11%

T7774H10PN 1996 4 1017 $1,149 $287.25 $151 $37.78 $ 36.94 $ 38.27 650.00%

1997 6 800 $1,791 $298.50 $173 $28.90 $ 28.26 $ 29.28 919.00%

1994 340 359 $715 $1.41 $800 $2.35 $ 2.30 $ 2.38 61.30%

T19MS4 1996 173 527 $293 $1.69 $428 $2.47 $ 2.42 $ 2.50 69.83%

1997 100 791 $141 $1.41 $185 $1.85 $ 1.81 $ 1.87 77.90%

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The results in Table 4-20 are indicative of a lack of data base integrity

given the extreme large variations between the actual values and those that

were computed by the model applied to the original data for each of the

periods. Another interesting observation concerns the commonly advanced

argument that traditional cost accounting methods tend to overcost high

volume products when compared to ABC overhead cost assignments.

Table 4-20 shows that, although the high volume product (13801) is over

costed, the low volume product (T7774H10PN) is also overcosted by a

substantial margin, whereas the medium volume product (T19MS4) is

under costed.

Organisational inventory records are unlikely to be manipulated to achieve

some desirable outcome and it, therefore, can be assumed that data base

inaccuracy is a result of indifferent data recording or general omissions.

Research evidence relating to data entry errors in general terms suggest

an error range of between 4% and 8% (Valenstein and Meier, 1999;

Swanson et.al., 1997; Stanton and Julian, 2002; Jørgensen and Karlsmose,

1998). The substantial number of errors detected in the database of the

organisation in both their inventory and production records was confirmed

by the management accountant and is usually adjusted at the end of a

period if detected. Error detection of recorded data, however, is not a

priority in the company’s operation.

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4.4 Chapter Summary

The analysis of three specific data bases (case studies) were selected for

their perceived data integrity and to test the robustness of the model

against actual, rather than random number generated, data bases.

Statistical analysis establishes the accuracy of data element attributes as

well as identifying domain consistencies. While the outcome of the analysis

was predicted, the results were still somewhat surprising.

The Stock Exchange data revealed data element inaccuracies, it confirmed,

however, domain consistencies. The data element inaccuracies are

surprising as daily transaction data is audited prior to the completion of the

trading day.

The university student enrolment records are the most difficult to explain.

W ith the exception of a single university most of the other universities

showed either data base inaccuracies or at worst both domain and data

record inaccuracies. Such findings should be of some concern especially

as a number of universities indicate domain inconsistencies which are

indicative that the recorded data does not come from the same university.

These findings maybe of interest to DEST as the public funding authority

for universities and their resource consumption.

174

The inventory data base also revealed data element inaccuracies but

showed domain consistency. Such finding was expected although inventory

records of public companies are audited prior to financial statement

publication.

Applying the computed model values to the inventory data base provided

the basis for overhead allocations that became situation specific. Earlier

analysis exposed that direct labour records were inaccurate and therefore

an inappropriate base for overhead allocations. As the majority of the

company’s product range consists of a 55% to 75% material cost

component the use of a material ranked distribution became an appropriate

cost driver for the overhead cost allocation.

Taking a random selected sample of high, medium and low demand

products further confirmed the claimed proposition of a more equitable

allocation method. Comparing the computed overhead allocations with the

existing overhead cost revealed under and over costed allocations. While

ABC comparisons with traditional cost allocation models consistently

demonstrate an over costed overhead allocation for high volume/low

complexity products and an under costed overhead allocation for low

volume/high complexity products (Pattinson and Arendt, 1994), the model

based allocation does not confirm such consistent variation. The inventory

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case study data shows that both high and low demand products are over

costed while medium demand products appear to be under costed when

compared with actual overhead cost data.

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5. Discussion of Results

In chapter 4 it was established that data base inconsistencies could be

addressed by the development of a model that allows the mirroring of a real

data base and use the model as a benchmark test for data base i tem

variation within acceptable boundaries. The parameters of the model were

based on the empirical evidence that almost all recorded data bases follow

an unbalanced item distribution that was first discussed by Pareto, W

(1883) and later picked up by Joseph Juran in the early 1950's as an

analytical approach in the development of quality improvement process.

While the general acceptance of a Pareto based accumulative data item

distribution remains valid, what had not been established is a model that

provides the basis for calculating the individual item contribution as a

method to predict pattern consistencies.

The model developed in Chapter 3 was tested and modified to insure its

robustness under varying data base parameters. Although, there is some

anecdotal (Roadcap et al., 2000) and some empirical evidence (Valenstein

and Meier, 1999; Swanson et al., 1997; Stanton and Julian, 2002;

Jørgensen and Karlsmose, 1998) that suggests data base integrity and

accuracy is diminished through data entry and data omission errors, there

is, however, little research that investigates the accuracy of an established

recorded data base. Given the acceptance that data entry and omission

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errors exist at a suggested level of between 4% and 8% (Valenstein and

Meier, 1999) it is surprising that there is very little effort to develop models

that allow analysis of existing data bases to detect the level of error that

exists.

To reduce the incidence of data entry and data omission errors in

developing the model, a random number generator approach was used to

establish the original data bases. The developed model was tested against

these data bases through pair wise comparison to establish its robustness

when applied to 3200 different data bases with varying parameters that

included changes in product pricing, product demand and distribution shape

factor. In addition the number of items were varied between 500 and 4000

to reflect medium size inventory levels.

To overcome the limitation of subjectively choosing the 20% focal point of

the (x) dimension a stratified selection of the random generated data bases

were used and additional focal points at the 10%, 30%, 40%, 50%, 60%

and 70% level were submitted to analysis to determine variations in error

levels. The range of error terms at any of these levels remained within the

original range at the 20% level. This analysis clearly established the validity

and robustness of the model and justified the subjective choice of the 20%

level as it is representative of the 20/80 rule discussed in other literature

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(Koch, 1998). A further comment on the use of a model that mirrors the

original data base is its variation at the point estimates. These point

estimates are useful to establish domain pattern similarities and also

provide the basis for comparison between original data base and model

generated data base. However, this function is limited to verify the integrity

of an existing data base and identify the level of variation for further

detailed investigation. A more important function of the model however, is

the ability to compute item contributions within the cumulative framework.

For this reason it is important to analyse and compare the differences in

item contribution rather than the item’s point estimate.

Item contributions are expressed in percentage terms and can be

ascertained by using part of the model [refer to (7)] developed. As

explained in detail in chapter 3 the first expression on the right side of the

model calculates the individual’s item contribution at a ranked sequence.

To illustrate this point, part of the model (7) is repeated here:

Using the values for c and d as shown in Table 4-19 in chapter 4 we are

able to calculate the percentage value of y i at xi. Using, for example, the

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1994 overhead data with a denominator value of 17.0471, a value for c of

7.116 and a value for d of .2668 we can calculate a percentage value of y i

given the rank of x i. in the example let x = 100, therefore:

This result enables the comparison between the accurate data base values

for each ranked data item and those values generated by the model in a

pair wise analysis. Point estimates compare the cumulative percentage

between actual and model data base values, which given the argument

provided earlier as to the likelihood and risk of data base inaccuracy due

to error entry and data omission would render such comparison as

meaningless and therefore the associated error term would not be

indicative of the robustness of the model.

The creation and testing of a substantial number of random number

generated data bases (3200 in total) revealed a consistency in both

domain identification and error term values that provides significant

evidence that the developed model is capable to detect inconsistencies in

“real” data bases and allows for the identification of element suspicion and

investigation. The model further, and more important, has shown sufficient

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robustness under varying data base sizes to be applied as a prediction

model for overhead determination of an organisation’s product portfolio.

The advantages from the developed model when compared to many of the

existing techniques used in the determination of overhead prediction is the

continuation of the preferred simplicity (Whittle, 2000) of the absorption

cost model with the added advantage of accounting for product additions

or deletions in a more equitable and product supportive approach.

While product additions are often allowed to add additional variable costs

to the existing costs of an organisation but, if added within the current

capacity level, will not incur any additional fixed overhead costs which will

be treated quite differently under various cost allocation techniques.

Under the absorption cost allocation approach direct labour or some other

single volume allocation base will be employed to compute an arbitrary

value of overhead costs applied to the new product. Variable costing

methods would only add the variable portion of the overhead to the new

product in an attempt to acknowledge that the fixed overhead total costs

remain unchanged within current capacity levels. Activity based costing

methods would identify the activities necessary in the production of the

new product and would use past activity cost data to attach overhead costs

to the product.

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Product deletions on the other hand are treated similar but with a cost

increasing effect on the remaining products within the organisation’s

product portfolio. This effect was demonstrated in Chapter 4 using the case

study data and the changing overhead costs of three products that were

part of the organisation’s product portfolio over the 4-year history

presented. Investigation of the inventory records revealed a product

retention rate over this period of approximately 70 percent using product

identification codes to determine product portfolio composition. The

inconsistency of applying overhead costs to products is clearly evident for

product 2 in Table 4-20 (T774H10PN) where overhead costs in 1994 were

$25.00 per unit but increased to 287.25 in 1996 and 298.50 in 1997. This

inconsistency, when pointed out to the management accountant of the

organisation at the time, was admitted as being erroneous. Other item

inconsistencies appeared across all the years that data was supplied.

Model calculated values for this item were more consistent and given the

general increases in material prices and labour costs over the period

reflects a more normal change in overhead costs on the basis of material

content.

This approach is a departure from general practice of overhead allocations

based on material content but was found to be the most acceptable

allocation base as material content on average exceeded 70 percent of the

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products’ costs. This departure also demonstrates the flexibility and

simplicity of the model to become situation specific rather then being a

general fit for all organisations. This general fit of overhead allocation

models (the most popular approach being the absorption cost model) on

the basis of single volume resource bases must be perceived as its major

shortcoming.

While Activity-based cost systems address this shortcoming of general

applicability and complement situation specific circumstances its system

design, however, is founded in the analysis of existing data bases and

subjective based cost driver determination. Furthermore, in chapter 2 it

was pointed out that the ABC suffers from similar problems to any of the

more traditional allocation techniques as the product and facility levels of

the ABC hierarchy also rely on judgement based overhead allocations in

addition to the discussed error creation from designing more disaggregated

cost data systems.

In addition, and as illustrated in chapter 2, different cost allocation methods

become greatly irrelevant, if the organisation pursues a profit optimisation

strategy by fully utilising its available resources. It can therefore be

conjectured that product cost profile determination is useful for single

product (line) decisions on the basis of resource opportunity costs if such

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decisions lead to increased profitability without a necessary increase in

available capacity. The problem of determining the appropriate overhead

costs for a single product within the totality of an organisation’s product

portfolio has been the subject of much discussion over the years with

different assignment models being available since the problematic nature

of the issue first surfaced. As survey evidence (Whittle, 2000) suggests

most organisations continue to use a simple allocation model to attach

general overhead cost to individual products but uses varying methods

when product related decisions are needed. Such continued persistence

with simplistic allocation models can also be construed as managements

perception that the complexity of an overhead cost assignment model does

not necessarily lead to either greater operational efficiencies or improved

profitability.

The arguments advanced in earlier chapters as to the irrelevance of using

different overhead cost distribution systems can also be leveled against the

proposed Pareto based overhead distribution model. W hat makes the

proposed system any better than ABC or traditional allocation models? The

response to this question is twofold. In the first place it has the ability to

test an existing data base for the integrity of its recorded data and in the

second place provides management with a complementary model similar

to the traditional absorption cost model that has retained its popularity

184

amongst management decision makers, despite the plethora of suggested

“better” overhead assignment models.

185

6. Summary and Future Research Suggestions

6.1 Summary

Research into data base integrity and accuracy has identified the existence

of data base errors being the consequence of numerous causes. Data entry

and data omission errors seem to be the most common causes for data

base inaccuracies. While the majority of the research evidence comes from

medical related publications in which inaccurate data can lead to disastrous

consequences, other data bases such as inventory records receive less

attention as these data bases do not fall within the same categories.

Furthermore, many of the financial data bases are to some extent protected

through the general accepted accounting principle (GAAP) of materiality

that allows organisations to accept inaccurate data base records if such

deviations fall within the acceptable materiality limits which in many cases

are set at the 10% level.

One of the most persistent problems in financial data bases and more

specifically in inventory records has been the application of the

contaminated data detail in the determination of product costs. Although

transaction records are available to verify the accuracy of material and

direct labour costs, overhead costs on the other hand have presented a

problem. As there is no direct connection between a product’s manufacture

(or a service provision) and an organisation’s related indirect costs of

186

resource consumption incurred in the manufacture of a single product,

allocations of these overhead costs were deemed necessary to compute

the total cost of a product. Various techniques for the allocation of an

appropriate amount of such indirect or overhead costs to each single

product or service have been developed and accepted over many years.

The inherent arbitrariness of these techniques has led to continuous and

ongoing criticism and encouraged the development of new techniques that

promise to reduce the arbitrariness factor in the overhead allocation

debate.

Activity-based costing, and to a lesser extent other methods grounded in

operations management, has gained considerable prominence in

contemporary organisational management accounting system designs but

have so far achieved only a limited implementation success. The reason for

such limited implementation by many organisations that are aware of the

claimed advantages of ABC proponents is difficult to explain. While recent

survey evidence indicates the continued popularity and application of the

more traditional and arbitrary overhead allocation methods it does not

explain the reason for rejecting many of the more contemporary overhead

cost system designs.

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Most of the evidence in support of the necessity to accept and implement

less arbitrary based overhead assignment systems (especially ABC) comes

in the form of case study and similar anecdotal evidence. A common basis

for much of these presentations is the reliance on the organisation’s

existing data records by extending data depositories. ABC is very specific

by insisting that a company’s current record system forms the foundation

of creating activity cost pools that serve as the basis for determining activity

costs by developing and defining appropriate cost drivers for the

computation of activity based costs. There is little evidence that the

establishment of the activity cost pools is free from any of the described

data entry and omission errors and thereby reduces the value of the

developed activity costs.

Other considerations and strategies pursued by organisations do not seem

to be suggestive of the importance of more “accurate” cost data in the

achievement of organisational objectives. A recent, partially longitudinal,

survey (Rigby, 2001) of management tools used does not indicate a

requirement or reliance on financial and management accounting based

data as a desirable tool in the decision making process of organisational

managements. This fact would support the proposition advanced in chapter

3 in which it was demonstrated that optimal profitability is not a function or

consequence of the cost accounting system employed by a company but

188

a function of capacity utilisation and product mix decisions. However,

product mix decision can be based on product cost data as well as capacity

resource consumption. Such considerations would require in most cases

a cost/benefit analysis to determine an optimal outcome.

If it is accepted that product cost data may not assume a dominant position

in management’s decision making process, it is, however, necessary to be

aware of product cost data for product mix related decisions. To

accommodate this desire of management, more reliable product cost data

becomes a prerequisite. When the discussion of distortions in product cost

data is approached, the arbitrariness of the overhead costs allocation

technique is presented as the major contributor to inaccurate product costs.

There is little, if any, discussion about the accuracy of the data collection

methods and the likelihood of corrupted data bases.

The concept of unbalanced or Pareto distributions has been used in many

situations for the analysis of pre-specified relationships of variables of

interest. Pareto analysis of data bases, however, has largely been defined

to a sorting of data elements to establish a dimensional ranking. While this

approach has provided a useful tool in determining value based

relationships it has, however, being restricted to a ranking tool. The ability

to mirror the element ranking contributions through a modeling approach

189

and analyse the paired differences for statistical significance provides a

basis for evaluating the integrity of the original data base. As it has been

suggested in the literature (Valenstein and Meier, 1999; Swanson et.al.,

1997; Stanton and Julian, 2002; Jørgensen and Karlsmose, 1998) most

data bases are likely to contain data recording and data omission errors,

which, given the reliance on such data bases may lead to inappropriate

evaluation of the information these bases contain. To overcome this

inherent risk of using existing data bases for developing a model that can

be tested for its robustness under varying parameter attributes a substantial

number random number generated data bases were used in the

mathematical modeling process. The application of a random number

generated data base provides the opportunity of changing various

parameters to reflect product characteristics as well and more importantly

eliminate the risk of data entry and data omission errors. The task of

developing a model that mirrors the unbalanced distribution of any ranked

set of data elements has further being assisted by the pre-specified use of

population data rather than representative sampling. The derived statistics

are therefore free from inference and more soundly based on population

parameters. The population statistics shown in Table 3-5 are clearly

indicative of the robustness of the model by the narrow band of error term

intervals across all 3200 data bases.

190

The choice and selection of the actual data bases used for analyses was

premised on the perception that these data bases should be free from error

or inconsistencies as their content is relied upon for decision making by

various groups. These groups include, investors, public funding authorities

and organisational management. It is therefore somewhat surprising that,

especially in the case of the public funding authority, no system of data

base integrity check is in place to verify the accuracy of the submitted data.

Inventory data may be considered as less critical in organisational decision

making as the issue of accurate product costing in a manufacturing

environment has not been resolved in a defensible way.

The case study examples clearly demonstrated that existing data bases

contain both domain and integrity errors. The choice of data bases was

selected on the presumptive perception of the level of data error incidence

that could be expected. W hile Stock Exchange data, given the sensitive

nature of its customers’ audience, should be thoroughly audited before

being made available to the public domain, evaluation of this data base

revealed data item inaccuracies. University data was suspected of being

unaudited before its submission to governmental funding agencies and

therefore reveal data inaccuracies. Not only did the university data reveal

data item inaccuracies but also revealed domain inconsistencies which

could be perceived as more serious revelation.

191

The organisational inventory case study example highlighted the incidence

of data inaccuracies that were compiled from production records. Although

the overhead allocation method used by the organisation followed the

absorption costing approach, distortions of product costs and inaccuracies

of recorded data could be traced to the data recording system, not the

overhead allocation method.

The allocation of overhead costs remains an unresolved issue.

Furthermore, the prescribed treatment of inventory valuations for

compliance requirements allows a number of techniques to establish total

inventory values with differing outcomes.

The model that was developed and tested appears to have the robustness

required to be a useful prediction model. The error term analysis further

confirmed the model’s ability to mirror an existing data base and detect

inconsistencies within the narrow confidence interval established. Once

data base consistency has been established prediction of individual

component characteristics or parameters can be accomplished. As the

overhead costs of an organisation are required to be assigned for both

inventory valuations and budget forecasts, the prediction model for the

assignment of these costs must be robust and credible. The organisational

inventory case study data used revealed a poor correlation between direct

192

labour hours and the resulting overhead cost allocations. A better and more

consistent data base was found in the direct material records that also

constituted almost 70% of the average product cost for this company. The

model was applied to allocate overhead costs and predict product costs for

subsequent budget periods and compared with the organisation’s budget

forecast. The resultant model based forecast compared favourable with the

traditional budget forecast although it was inappropriate to suggest which

of the two forecasts was more credible. The part of the forecast that related

to product costs’ indicated discernable differences but could be explained

by the previous detected but uncorrected inaccurate production cost data.

The model developed and depicted (model (7), p.130) differs from other

established overhead assignment methods in that it reflects the unbalanced

distribution of data bases and does not follow the accepted assumption of

linearity. The most common data analysis and subsequent prediction

approach, as found in any of the management accounting texts, assume

that a standard linear regression method provides the best fit for the

overhead cost data of organisations. If this assumption is accepted then

changes in a company’s product mix through product additions or deletions

without changes in capacity availability will lead to erroneous product cost

computations by maintaining the established volume based allocation

algorithm. The model provides a greater flexibility in determining the

193

appropriate allocation base and allows for the redistribution of established

dimensional criteria after product mix changes.

6.2 Major Contribution

Confirmation of unbalanced distributions in data bases (Koch,1998)

provided the basis for the development of a model, using computer based

mathematical modeling techniques, that mirrors the shape of the cumulative

distribution curve. Although, a generalised Pareto distribution model for the

determination of fat and thin tail distributions exists, a model for the testing

of point and interval characteristics of data elements for the entire

population could not be found in the literature. Statistical testing of the

model validated its robustness under varying parameter settings. In

pairwise comparisons between the data elements of the actual data base

and the model based computed values, data element inaccuracies and

domain inconsistencies can be detected to instigate corrective action.

In addition, the developed model was applied in the assignment of

overhead costs to individual products on a non linear basis which, given the

confirmation of unbalanced non-linear data base distributions, provides a

more accurate allocation method than currently applied overhead

assignment techniques that rely on linear relationship assumptions. The

relative simplicity of the model in assigning overhead costs to individual

194

products complements current practices that rely on very traditional

absorption cost allocations.

6.3 Future Research Suggestions

The model developed in this thesis clearly demonstrates the existence of

unbalanced distributions in most if not all collected data bases. The

incidence of data entry, omission and related errors that are a natural

consequence of data compilations requires a method for testing the level

of data corruption in a post hoc situation. Many of the contemporary

overhead assignment techniques are reliant on an organisation’s existing

cost data base for reassignment rather than reallocation of overhead costs.

Even though many of the proponents for changing traditional overhead

allocation techniques rely on case data to illustrate differences in cost

profiles between the “new” and the traditional methods, none seems to

question the accuracy of the compiled data.

The relative importance of the overhead assignment technique adopted by

an organisation, is based on the desire to establish budget forecasts that

predict resource requirements for the forecasted period. Traditional

overhead allocation techniques have produced substantial variances when

actual and forecasted results are compared for operational feedback. As

the majority of these techniques rely on linear prediction models, such

195

variances should be expected. Furthermore, the prediction of product costs

is often aggregated by product groups and thereby introduces further

forecasted distortions.

At the operational forecast level more detailed product cost data is utilised

to translate the broader corporate forecast into operational data of

individual product costs and resource requirements. It is at this level that a

more accurate predictive model is required. With current computer

technologies it is no longer a barrier to investigate and re-rank complete

data bases to conduct timely analyses. The model development could be

extended to detect item inconsistencies on the basis of paired comparisons

for recorded data but not for omitted data. Data omissions are difficult to

detect but a refinement in the domain profile analysis could reveal

inconsistent item rankings.

Given the lack of models to test data base accuracy, it is of benefit to

further develop models that are capable in detecting data compilation

errors. These models would particularly assist in financial record analysis,

medical and pharmaceutical data base analysis and any data base that

forms the foundation for decision making.

196

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List of Publications by Author relating to Thesis

REFEREED ARTICLES

Fechner, H.H.E., (2000) ““O Custeio Baseado Em Atividades Pode Ser MelhoradoPela Análise ABC?”,Revista Do Conselho Regional De

Contabilidade Do Rio Grande Do Sul, November, pp.18-32. Fullpaper translated by by Jose A. M. Pigatto and Ivan H. Vey.

REFEREED CONFERENCE PAPER PRESENTATIONS

Fechner, H.H.E. (2001) “The Application of Pareto’s Principle to assign OverheadCosts to establish Product Cost Profiles”, 13th Asia Pacific

Conference on International Accounting, Rio de Janeiro,October

Fechner, H.H.E. (2001)”The (Ir)relevance of Cost Management Systems inDetermining the Optimal Product Mix of An Organisation.”,The

British Accounting Conference, Nottingham, UK, March

Fechner, H.H.E. (2000) “Choose the Right ABC as Basis for Your StrategicManagement Accounting System.”, 2nd European Management

Accounting Conference, Brussels, Belgium, December.

Fechner, H.H.E. (2000) “Data Base Pattern Consistency as a Foundation ofBenchmark Standards and the Development of Product CostProfiles.”,12th Asia Pacific Conference on International

Accounting, Beijing, October.

Fechner, H.H.E. (2000) “Analysis of Overhead Allocation Patterns with theApplication of the Pareto Principle.”,10th Annual Conference of

Accounting Academics, Hong Kong, (June)

Fechner, H.H.E. (2000) “Overhead Allocation Problems Revisited: Arbitrary or

Equitable.” The British Accounting Conference, Essex, UK,

March

Fechner, H.H.E., (1998) “Can Activity Based Costing be improved by A-B-CAnalysis”, 21st Annual Congress of the European Accounting

Association, Antwerp - Belgium, (April)

Fechner, H.H.E., (1997) “Does Activity Based Costing create optimal Product CostProfiles”, 9th Annual Conference of Accounting Academics,Hong Kong, (June)

This paper was awarded the best sectional paper prize.

203

Fechner, H.H.E., (1997) “Reconciling Activity Based Costing with StrategicManagement Accounting”, 20th Annual Congress of the

European Accounting Association, Graz, Austria, (April)

Fechner, H.H.E., (1996) “To implement or not to implement Activity Based Costing:A Question of Costs”, 8th Asia Pacific Conference on

International Accounting Issues, Vancouver, Canada, (Nov)

Fechner, H.H.E., (1996) “Activity based Costing (ABC): Universally adoptable orselectively applicable?”, 19th Annual Congress of the European

Accounting Association, Bergen, Norway, (May)

Fechner, H.H.E., (1995) "Advanced Manufacturing Technologies - An Industrychoice: A case for retaining traditional management accountingpractices", 7th Asia Pacific Conference on International

Accounting Issues, Seoul, Korea, (November)

Fechner, H.H.E., (1994) “The Influence of Advanced Manufacturing Technologieson Management Accounting Systems Design", European

Accounting Association Congress, Venice, Italy, (April)

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