Dynamic Modelling Scm

A Flexible and Generic Approach to Dynamic Modelling of Supply ChainsAuthor(s): W. Y. Hung, S. Kucherenko, N. J. Samsatli, N. ShahSource: The Journal of the Operational Research Society, Vol. 55, No. 8 (Aug., 2004), pp. 801-813Published by: Palgrave Macmillan Journals on behalf of the Operational Research SocietyStable URL: http://www.jstor.org/stable/4101807 .Accessed: 22/05/2011 23:54

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A flexible and generic approach to dynamic modelling of supply chains

WY Hung, S Kucherenko, NJ Samsatli and N Shah*

Imperial College, London, UK

In this paper, we present a new modelling approach for realistic supply chain simulation. The model provides an experimental environment for informed comparison between different supply chain policies. A basic simulation model for a generic node, from which a supply chain network can be built, has been developed using an object-oriented approach. This generic model allows the incorporation of the information and physical systems and decision-making policies used by each node. The object-oriented approach gives the flexibility in specifying the supply chain configuration and operation decisions, and policies. Stochastic simulations are achieved by applying Latin Supercube Sampling to the uncertain variables in descending order of importance, which reduces the number of simulations required. We also present a case study to show that the model is applicable to a real-life situation for dynamic stochastic studies. Journal of the Operational Research Society (2004) 55, 801-813. doi:10.1057/palgrave.jors.2601740 Published online 14 April 2004

Keywords: supply chain management; simulation; stochastic; system dynamics

Introduction

It is said that the only constant in today's dynamic business environment is change.' Regulatory changes, globalization, increasing intensity in competition, increasingly demanding customers, new information technology, and mergers and acquisitions have been prompting improvements in supply chains of various industries, including those of the process industries, in order to stay ahead of the competition. There is even an axiom highlighting its importance: 'a 1-cent reduction in supply chain costs can have as much as a 5-cent improvement on operating profits'.2 Supply Chain Management (SCM) has thus drawn a lot of attention in the academic and business world. In practice, efficient consumer response in the grocery industry, efficient healthcare response in the healthcare industry, and quick response in the textile industry are examples of SCM tailored to meet the needs of the particular industries.

The term SCM has been broadly used in the literature with various meanings due to the development of the philosophy from various perspectives: purchasing and supply; transportation and logistics; marketing; and level of coordination. Although different in origin, these theories have now merged into a holistic and strategic approach to operations, materials and logistics management. A definition

given by the SupplyChain.com (http://www.thesupplychain. com) is

'SCM is a strategy where business partners jointly commit to work closely together, to bring greater value to the consumer and/or their customers for the least possible overall supply cost. This coordination includes that of order generation, order taking and order fulfilment/distribution of products, services, or information. Effective supply chain management enables business to make informed decisions along the entire supply chain, from acquiring raw materials to manufacturing products to distributing finished goods to the consumers. At each link, businesses need to make the best choices about what their customers need and how they can meet those require- ments at the lowest possible cost.'

In other words, the purpose of SCM is to deal effectively with external strategic changes, such as globalization, and operational uncertainties, such as demand fluctuations, in order to take advantage of any new opportunities, and to drive down the overall supply costs. Since the cost of changing a business strategy and operational policies can be huge, it would be wise to have a simulation model of the supply chain network concerned so that various strategies and policies can be evaluated and compared quantitatively before being implemented on the real business.

Since the time correlation of upstream and downstream operations is key to the success of SCM, dynamic studies are particularly important in supply chain improvements. With dynamic stochastic models, it is possible to assess the effects of various uncertainties on the overall performance mea- sures, discover where the real bottleneck is and avoid

*Correspondence.: N Shah, Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College, London SW7 2AZ, UK. E-mail: n.shah@ aimperial.ac.uk

802 Journal of the Operational Research Society Vol. 55, No. 8

investing unnecessarily. These models also allow the design of more responsive yet easy to implement production and inventory management systems to accommodate inevitable external changes and uncertainties, without making the systems too lean and hence fragile.

Furthermore, according to Lambert and Cooper,3 the supply chain structure can be changed by decision-making. Examples are that moving from multiple- to single-source suppliers will narrow the supply chain, or that outsourcing logistics, manufacturing, marketing or product development activities may increase the length and width of the supply chain. They also found that the overall supply chains look different from each company's perspective, since the management of each company sees its firm as the focal point of the supply chain and views the membership and network structure differently. Hence, it will be useful if the model is flexible enough to allow easy reconfiguration.

This paper presents a new modelling approach based on object-oriented dynamic modelling to enable dynamic stochastic studies on supply chains. The remainder of this article is organized as follows. The second section gives a review of the literature on supply chain modelling approaches. The third describes the new modelling approach developed. The fourth outlines the simulation procedures with the use of the new modelling approach. The fifth shows the benefits and insights achieved with this modelling approach in a case study. Finally, the last section concludes the work and presents the future steps planned.

Literature review on supply chain modelling approaches

Analytical models versus simulation models

There are two main categories of supply chain modelling approaches that help decision-making: (1) analytical, or mathematical, models, and (2) simulation models.

The purpose of analytical models is to maximize certain benefits by optimizing some aspects of the supply chain. Previous work on analytical models can be further classified into two main categories in terms of what they optimize: (i) the strategic design, and (ii) the operation. Strategic design can involve the determination of suppliers and market segments to serve, the number, location, capacity and type of a company's facilities, the amount of various materials to produce and hold at different supply chain members and shipped among them, and/or the routing of material flows. With regard to operation optimization, the aspects con- cerned can be inventory management at various points along the supply chain network, and/or production planning and scheduling. For more information on analytical supply chain models, see the reviews of Vidal and Goetschalckx4 and Beamon.5

Although analytical models can be useful in many cases, there are some instances where they are too simplistic to be of practical use for complex supply chains. Simulation

models allow a more realistic capture of the supply chain characteristics and provide a means to evaluate the impact of policy changes carried out by one or more supply chain members. Therefore, simulation models can be used to verify changes in the supply chain or its policies, and as an important first step towards realistic optimization. This paper is concerned with simulation models only.

Previous work on simulation models

Slats et a16 propose the building of logistic laboratories to conduct various experiments regarding the integration and design or redesign of logistic chains, so as to improve the performance of the total logistic chain. Their model involves linking building blocks together to give the structure of the logistic chain. However, the laboratories proposed are for simulating and designing only the distribution network for end-customer goods, and do not consider the supply chain network as a whole. Moreover, the laboratories are in the form of software packages that are not easy for the user to alter or to extend the functionality of the models.

Alfieri and Brandimarte7 present a small case study using an object-oriented methodology to extend the idea of the logistic laboratory proposed by Slats et al.6 They claim that the object-oriented approach is well suited to the modularity requirements in the logistic laboratory, because there is a better transition from modelling concepts to actual software implementation since objects have a natural match in the real world. Although their model illustrates the usefulness of multiple inheritance and dynamic method binding in developing the building blocks in a logistic laboratory, it is too simplistic to represent real-world situations.

Yu et a18 introduced a more sophisticated, reusable enterprise model, called a factory data model (FDM), based on an object-oriented approach. The model is claimed to be reusable, because when the information content is overtaken by fast changing market conditions, new models can still use part or all of the information from previous models. Five essential information classes are identified: strategy, re- source, process, flow, and token, each of which heads a hierarchy of subclasses. However, their primary aim is to aid business process redesign only within one enterprise, and hence they do not consider activities in other parts of the supply chain.

A dynamic modelling approach from the Process Systems Engineering viewpoint is proposed by Perea et al9 and claimed to enable the design of systematic decision-making processes for the supply chain. They capture the supply chain dynamics by the balance of inventories and the balance of orders in terms of ordinary differential equations, together with the definition of shipping rates to the downstream product-nodes, subject to some physical bounds and initial conditions for the inventory and order values. The drawback of this simulation model is that it assumes the

WY Hung et a/l--Dynamic modelling of supply chains 803

material and order flows to be continuous; in reality, they are often discrete events.

van der Vorst et al 10 present a discrete-event supply chain model based on timed coloured Petri-nets, a graphical- oriented language with concurrency. Their model comprises four types of component: business processes, performance indicators, design variables, and business entities (similar to the token class mentioned above). Discrete-event simulation is employed to model the dynamics of the supply chain. Despite the detailed modelling, the model considers only the distribution of end-customer goods and does not take into account other upstream supply chain processes.

Gjerdrum" presents a stochastic discrete-event simulation model for a supply chain with three echelons: primary manufacturing, secondary manufacturing, and demand management. The model also considers uncertainties in market demand and machine breakdowns via Monte Carlo (MC) sampling. Each echelon is modelled separately and differently to simulate the real situation. Since the model is tailor-made for one particular supply chain, it is not easily modified.

Research objectives

While detailed, realistic, dynamic, flexible simulation models are needed to analyse the complex situation across supply chain members, existing models are limited by a number of assumptions, focus on only one certain part of supply chain, or are not sufficiently flexible to allow easy exploration of innovative policies. This paper presents a new supply chain modelling approach that allows easy and quick model building for exploring various supply chain options. Using this approach yields models that are flexible and sufficiently detailed to enable realistic simulation of stochastic discrete events.

Description of the modelling approach

Modelling concepts

To give the flexibility in the model supply chain configura- tion, a supply chain network is modelled as a group of connected 'nodes', each of which resembles an individual physical facility, such as plants, warehouses, or retailers. A generic node is developed that can represent each type of facility with its attributes characteristic to the individual node to be specified by the user. Therefore, the generic nodes are viewed as the building blocks of a supply chain network, connected to each other with a customer-supplier relation- ship, which resembles the real physical situation.

Each node can be composed of three main components: Inbound Material Management, Material Conversion, and Outbound Material Management. These three components are equivalent to the material control, production control, and finished goods stockpile submodels described by Cohen

and Lee.12 While they regard the three submodels as having fixed control mechanisms to obtain optimal values of parameters for total cost minimization, here the three components simulate the policies employed within one physical facility, and are specified by the user. The user can opt for selecting only the Inbound Material Manage- ment and Material Conversion if the outbound materials are

shipped direct to another facility (ie the node concerned does not hold any outbound material inventory), or selecting only the Inbound Material Management if there is no conversion process within the facility. Between the nodes a list of materials flows downstream and a list of orders flows upstream. This concept is shown in Figure 1.

The function of the Inbound/Outbound Material Man- agement is to control the stock levels of a group of inbound/ outbound materials such that their requirements by the Material Conversion/downstream nodes can be met (ie no stock out) without holding excessive stocks. The stock level of each material is to be controlled by a particular replenishment control policy due to different item profit contributions as a result of sales popularity, importance of the specific item to the overall product line, profitability and the value of the merchandise, and because of different policy administrative costs.1,13,14 The Inbound Material Manage- ment replenishes the stock levels by issuing orders to one or more upstream nodes, whereas the Outbound Material Management does so by issuing orders to the Material Conversion component within the same node. The various replenishment control policies found in the literature (see Table 1) can be implemented in the Material Management components.

The function of the Material Conversion component of a node is to plan production and determine when the orders can be fulfilled, subject to some specified resource constraints and manufacturing logic. It implements a process that converts a certain amount of inbound materials to a certain amount of outbound materials, based on a recipe. This can represent a production or packaging process in a plant, a packaging breakdown and/or sorting process in

Generic Node Material flow

IMM MC OMM

Order flow

where IMM = Inbound Material Management, MC = Material Conversion, OMM = Outbound Material Management.

Figure 1 Generic node concept.

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a warehouse, or a transportation process that alters the location of the items. Before processing the orders, a priority-sequencing rule, such as earliest-due-date (EDD) or first-come-first-served (FCFS), is employed to sort the orders. For the process itself, optimized production technol- ogy (OPT) or any other planning algorithm may be adopted. In the case of outsourcing the process to a contractor, the resources available to the parent company may be treated as limitless.

Generic node model structure

To design the model structure, an object modelling technique (OMT) object model class diagram of the generic node is written. OMT is a solution design methodology that comprises object models, dynamic models, and functional models. The object model is used here as it describes the structure of the system.'5 Classes are generalizations of certain objects that share the same data structure and behaviour.

The OMT object model class diagram of a generic node, consisting of the three main components of Inbound Material Management, Material Conversion and Outbound Material Management, which in turn comprise other components, is presented in Figure 2. The associations that allow for the two- and one-component nodes to interact with

Table 1 Various replenishment control polices

Replenishment control policies

(a) Re-order point (ROP) techniques (b) Material/distribution requirements planning (MRP/DRP) (c) Base stock control (BSC) (d) Line requirements planning (LRP) (e) Vendor managed inventory (VMI) (f) Just-in-time (JIT)

other nodes are not shown here for clarity. For the generic node in Figure 2, the associations among the components are described in the Appendix. The upstream order flows are simulated by order objects being created by the replenish- ment control policy concerned and accessed by an upstream node or component. The downstream material flows are simulated by updating the related stock levels after the orders are processed by an upstream node component.

Replenishment control policies

Replenishment control policies are used in the Inbound and Outbound Material Management components of a supply chain node to control the stock levels of various SKUs kept in the node. The various replenishment control systems that can be modelled are shown in Table 1. They can be classified according to whether they are instantaneous or time-phased (dynamic), whether they consider only local inventory or integral inventory (including stock in transit and at other nodes downstream), and whether they are push (based on demand forecasts) or pull (based on actual customer demands) systems. Here we describe the more common replenishment control policies, which have been incorpo- rated into our model: re-order point techniques (ROP) and material/distribution requirements planning (MRP)/(DRP).

ROP techniques consider the inventory position of a material at one location at one point in time. Hence, they are instantaneous, local inventory, pull systems. ROP techniques can be divided into four types; further categorized as continuous review and periodic review. The two continuous review policies are:

* Reorder-point, reorder-quantity (s, Q) system: a fixed quantity Q is ordered from an upstream node when the inventory position drops to or below the reorder-point s.

Generic node

Inbound material Material Outbound material management

consumes/ conversion computes management produces

, expected

keeps

dueddces

customer Inbound SKU Resource Recipe Outbound SKU supplier

replenishment I I replenishment

Replenishment maintains issues

control policy triggers Internal order container

F- Inventory Order

ROP MRP/DRP .. SKU ID

External

Internal-m by External order container

Figure 2 OMT object model class diagram of the generic node.

WY Hung et a/-Dynamic modelling of supply chains 805

* Reorder-point, reorder-up-to-level (s, S) system: a vari- able size replenishment is made to raise the inventory position to the reorder-up-to-level S when the inventory position drops to or below the reorder-point s.

The periodic review policies are:

* Periodic-review, reorder-up-to-level (R, S) system: for every R units of time, enough is ordered to replenish the inventory position to the reorder-up-to-level S.

* (R, s, S) system: this is a combination of (s, S) and (R, S) systems.

MRP and DRP deal with the management of current and future inventory levels, based on demand forecasts at one location. Therefore, they are time-phased, local inventory, push systems. MRP and DRP work by the same mechan- isms; their difference is that MRP is employed to manage raw materials for production planning, while DRP is used to manage finished goods.16 Considering the existing customer orders, forecast demand, process recipe, current inventory levels, planned inventory receipts and lead time require- ments, it produces a schedule of planned orders to be issued. Closed loop MRP includes capacity checks as an enhance- ment to produce feasible plans. Manufacturing Resources Planning (MRP II) has the same inventory management approach as closed loop MRP, with the additional enhancements to convert the outputs of production planning and control into financial terms and to draw on forecasts from other departments within the firm.13

The basic principle of MRP is as follows. The demands for each material are forecasted on a discrete time and these demand forecasts are called the gross requirements. For an outbound material, its gross requirements are the sum of the demand forecasts from all of its customers. With regard to an inbound material, its demand forecasts are derived from the demand forecasts of those outbound materials that consume it in the associated process recipes, offset by the conversion lead time. The net requirements at various future time steps for a material are estimated from the equation: N,=max (0, G, + SS,-It1-PR,), where N, is the net requirements at period t, Gt the gross requirements for period t, SSt the safety stock (reorder) level at period t, Itt1 being max {0,

It-l}, where It-1 the inventory at period

t-1, and PRt the proposed receipt at period t. Orders are issued in advance for the periods with non-zero net requirements. In practice the order quantities are discrete values (eg minimum order quantity + n order increments). This results in a master schedule, which is reviewed at every time step.

Simulation

Overall simulation procedure

In the initialization step, the supply chain structure is defined by specifying the facilities involved as nodes and then linking

them together. Within the simulation loop, stochastic dynamic simulations are carried out to compute the expected performance measures, by sampling the uncertain product demands from their respective probability distributions for each time period within the planning horizon, and creating orders with regard to the policies employed and their parameters as well as pulling the materials accordingly along the supply chain. The overall simulation procedure is shown below.

* Initialization:

o Define the node structure for the supply chain. o Specify the initial states of each node such as the SKUs

it holds, the corresponding replenishment control policies for these SKUs and so on.

o Specify demand forecasts for each SKU, if required by the particular replenishment policy.

* Start of simulation loop (n=l to the number of simulations) o Create 'real' demands for final products by sampling

from their respective probability distributions (eg normally distributed about the forecast value).

o Specify initial orders for t = 1. o Start of time loop (t = 1 to the planning horizon length)

- End-customers pull the final products. - Examine the stock level of each SKU held within

each node and issue replenishment orders accord- ing to the corresponding control policy.

- For each production site, sort the received orders, produce the required SKUs and deliver them to its customers.

- Record the stock level for each SKU at this time step and perform stock carryover to the next time step.

- Increase the time by one (t t + 1). o End of time loop o Reinitialize the nodes (eg clear orders, reset SKU stocks

to initial values etc.). o Increase the simulation counter by one (n = n + 1). o End of simulation loop

Sampling technique for the stochastic very high dimensional simulations

Dynamic supply chain models often involve many uncertain variables, such as the varying demands of a number of products at many future time periods. The number of uncertain variables can easily reach the range of hundreds. Stochastic simulation of such a high-dimensional problem often consumes a lot of computation time because of the large number of samples required, and thus the need for efficient sampling is pressing.

It has been recognized through theory and practice that a variety of uniformly distributed deterministic sequences provide more accurate results than purely random samples

806 Journal of the Operational Research Society Vol. 55, No. 8

of points. The low-discrepancy sequences (LDS) are designed specifically to place sample points as uniformly as possible. Unlike random numbers, successive low-discre- pancy points 'know' about the position of their predecessors and fill the remaining gaps. LDS have been used instead of random numbers in evaluating multi-dimensional integrals and simulation of stochastic processes - in the areas where traditionally MC methods were used.17,18 It has been found that methods based on LDS, known as quasi-MC (QMC) methods, have performance superior to that of MC methods on certain integrals. The improvement in time-to-accuracy using QMC can be as large as several orders of magnitude.

However, it is generally reported in the literature that for high-dimensional functions (ie number of dimensions > 12 or 15) QMC methods lose their advantage over MC (quoted by Owen'9 and Sobol'20). For very high-dimensional problems, Owen21 introduces Latin Supercube Sampling (LSS), which uses an MC technique to improve QMC. In LSS, the input variables are grouped into subsets, and within each subset QMC points are applied in random order. Some numerical experiments are conducted to compare the accuracy of LSS with those achieved with MC, using two integrals from Morokoff and Caflisch.21 The low discre- pancy quasi-random sequence used in LSS subsets is the Sobol' sequence22 and the pseudo-random sequence used in MC is the improved initialization version of the Mersenne Twister23 algorithm (http://www.math.keio.ac.jp/- matu- moto/emt.html). The results show that for 360 equally important dimensions, the accuracy of LSS can be significantly better than MC for the same number of sampling points (Figures 3 and 4). Therefore, for very high-dimensional problems, LSS is a good sampling method for faster convergence.

In the case of supply chain modelling, unlike simple mathematical integrals, the true values of the mean and variance of the outputs for a particular set of supply chain policies within the specific supply chain structure are often unknown. Since we are interested in the expected output values, we take a fixed number of samples in an attempt to approximate the probability distributions of the uncertain input variables and compute the mean output values. This process is then repeated over a number of runs to obtain a number of mean values for the outputs concerned. With the mean values from a number of runs we calculate the standard error of the mean and an overall mean for each output value. When the standard error of the mean is less than 1% of the overall mean of the output value, we consider the mean output value to have converged.

Model validation

The case study is based on an actual supply chain of a leading pharmaceutical manufacturer. Prior to the studies described in the next section, a pilot study was performed, in which the model was tested against historical data from the

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Figure 3 Root-mean-square integration error for F-= -I= 1(1 + 1/s)x!Is, where s = 360.

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Figure 4 Root-mean-square integration error for F= H]f= l(s-xi)/(s-0.5), where s - 360.

PLOT TYPES A 1C~r

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1084

a 4

?71

F, 1? 19 21 23 25 27 29 31 33 3? 37 39 41 43 45 47 49 51 S3 SS S7 59 (1 U G5 Gi 69 71 73 7& 77 79 Turntidayts)

Figure 5 Model validation in a pilot study; the faint lines are actual data and bold lines are model predicted data.

real supply chain. The comparison of the model predictions and actual data is shown in Figure 5. In general, the model fits the data quite well. The discrepancies are thought to be mainly due to human factors in the implementation of the business processes.

WY Hung et al-Dynamic modelling of supply chains 807

Case study

Description

To demonstrate the applicability of the new modelling method, the supply chain network of a fairly vertically integrated multinational pharmaceutical company is simu- lated. Based on its existing inventory management and production policies, the aim is to estimate for two of its final products to its external customers: customer service level (CSL); probability of stock out (PSO); average inventory (INV), and stock levels over a time horizon of 2 years. In particular, the customer service level (CSL) is taken to be the fill rate, which is the total quantity sold over the total quantity ordered, for that SKU market for the whole time horizon (104 weeks) averaged over all the simulations. When the stock level is lower than the order quantity, only the stock available is sold with no backorders allowed.

Figure 6 shows the simulated supply chain network configuration and the locations of the various inventories. There are two markets and four final products: Packs A and B are to be sold in the Japan market; Packs C and D are to be sold in the USA market. All of these final products are made from an Active Ingredient (AI). Packs A and B are produced in a plant in Asia, while the production of Packs C and D are carried out in a plant in America. The production of Packs A and B is simulated as two steps: (1) AI is used to produce Tablet A, Tablet B, Tablet EurExp, and Tablet GenExp, then (2) Tablets A and B are packaged to give the final SKUs Packs A and B, respectively. Tablets EurExp and GenExp are bulk products to be exported without packing. AI, the ingredient for the Tablets, is in turn produced in a plant in Europe through five synthesis stages. Stockpiles of the intermediate materials produced from each stage are kept in the European plant as buffer stocks.

With the generic node modelling approach described in the previous section, the supply chain structure is simulated

using nine nodes in total, each representing a distinct facility. Each Demand Management activity and reaction is repre- sented by one node, the Asia Secondary Manufacturing by two nodes due to the separate simulation of tablet production and packaging, the America Secondary Manu- facturing by one node, and the Europe Primary Manufac- turing by four nodes due to its four trains of equipment.

The policies and parameters of each component in the individual nodes are listed in Tables 2 to 8. In particular, the replenishment policy type for the intermediates within the nodes in the European primary manufacturing site is a customised type called DynTarget, in which the stock level is monitored continuously and orders are issued whenever the stock level is below the specified target stock level. The order quantity is proportional to the difference between the stock level and the target stock level. MRP/DRP are used for the replenishment control policies of the tablets and the final products. Here, a dynamic safety stock point is used for each MRP/DRP managed material to cover the demand forecast (or gross requirements) for a number of time steps, d, ahead, such that the safety stock point at period t, SS,, is given by SSt t+d-1 G . Orders are then issued in advance if the estimated stock level is below the safety stock point at that future time, or cancelled if the forecasted stock level is higher than the maximum level to prevent overstocking. The time horizon is divided into three periods as shown in Figure 7: frozen, scheduling, and planning. No orders with a requested due date within the frozen period can be issued unless they are 'emergency' orders. Orders with a requested due date within the scheduling period can be issued or cancelled depending on how the estimated stock level changes due to the actual demand being different to the forecast. Orders

Primary Manufacturing Secondary Manufacturing Demand Management

Asia 1 Asia 2Jan 0 1

2 AI I TA,wTB,

eek PA, PB

Europe 1 Europe 4/5 I week T

' P, PB

I C I C O 0m

ds RM 13 14

TAATTEE, TGE

demands

Euroe 2 Euro e3 America USA 0 2 PC, PD

I C week weeks C 1 weel demands IAl PC PD .

Key: I = Inbound Material Management, C = Material Conversion, O = Outbound Material Management RM = raw material, In = Intermediate n, AI = active ingredient, TA = Tablet A, TB = Tablet B, TEE = Tablet EurExp, TGE = Tablet GenExp, PA = Pack A, PB = Pack B, PC = Pack C, PD = Pack D

Figure 6 Supply chain network configuration for the case study.

808 Journal of the Operational Research Society Vol. 55, No. 8

Table 2 Replenishment control policies for the final products

Node Japan USA

SKU stock Pack A Pack B Pack C Pack D

Replenishment policy type DRP DRP DRP DRP Safety stock level (weeks) 4 4 4 4 Minimum order quantity (packs) 3000 2000 5000 20000 Order increment (packs) 3000 2000 5000 20 000 Maximum order quantity (packs) 9000 8000 45 000 40 000 Maximum stock level/safety stock level (%) 145 145 145 145 Initial stock level (packs) 15 000 15 000 60 000 60 000

Table 3 Replenishment control policies for the tablets in Asia Secondary Manufacturing

Node Asia 2

SKU stock Tablet A Tablet B Tablet EurExp Tablet GenExp Replenishment policy type MRP MRP MRP MRP Safety stock level (weeks) 3 3 3 3 Minimum order quantity (packs) 10 000 10 000 10 000 10 000 Order increment (packs) 10 000 10 000 10 000 10 000 Maximum order quantity (packs) 200 000 200 000 200 000 200 000 Maximum stock level/safety stock level (%) 135 135 135 135 Initial stock level (tablets) 2 x 106 2 x 106 2 x 106 2 x 106

Table 4 Replenishment control policies for AI in Asia and America Secondary Manufacturing

Node Asia 1 America

SKU stock AI AI Replenishment policy type ROP: (s, S) ROP: (s, Q) Safety stock level (kg) 200 150 Minimum order quantity (kg) 10 130 Order increment (kg) 10 0 Order-up-to-level (kg) 300 Initial stock level (kg) 200 180

with a requested due date within the planning period are not considered in detail.

Demand forecasts for a horizon of 104 weeks are available for the final products Packs A, B, C and D, as well as for Tablets A, B, EurExp and GenExp. The real demand for each final product at each time step (ie week) is uncertain and can be represented as any appropriate type of

probability distribution. In this case it is taken to be of a normal distribution with the mean y being the forecast value G, and the coefficient of variation c being a function of y and the maximum forecast value for that product over the horizon, (Mmax - maxt G,) : c = 1.0 - 0.8(P1/Mmax). There-

fore, the demand is N(u, cyl). Market demands for Tablets EurExp and GenExp are assumed to be the same as the forecasts, which in real life can correspond to having fixed supply agreements with some customers, such as Govern- ment bodies. There are 4 x 104=416 uncertain variables (ie the market demands of the four final products at 104 weeks). This is a very high-dimensional problem and LSS is applied for the stochastic simulations.

Simulation cases

In addition to the base case described above, we have simulated two more cases to test the system's responsiveness to inaccurate forecasts and one more case to examine the

Table 5 Replenishment control policies for the intermediates in Europe Primary Manufacturing

Node Europe 1 Europe 2 Europe 3 Europe 4/5

SKU stock Raw material Intermediate 1 Intermediate 2 Intermediate 3 Intermediate 4 AI Replenishment policy type DynTarget DynTarget DynTarget DynTarget DynTarget Target stock level (kg) 1200 1200 2000 2000 1600 Order proportional constant 1 1 1 1 1 Intial stock level (kg) 9 x 106 1000 1000 2000 2000 1500

WY Hung et a/-Dynamic modelling of supply chains 809

Table 6 Details of the conversion processes for the final products

Node Asia 2 America

Recipe 12 Tablet A in 30 Tablet B in 600 mg AI in 900 mg AI in one Pack A one Pack B one Pack C one Pack D

Production rate (packs/h) 600 1200 Nominal production time (h/week) 40 60 Overtime allowed (h/week) 20 15 Unavailabilitya 0.1 0.1 Downtime multipleb 3 3

aUnavailability is the probability of equipment breakdown based on historical data. bDowntime multiple represents how many times longer to process an order during the equipment breakdown or downtime.

Table 7 Details of the conversion processes for the tablets in Asia Secondary Manufacturing

Node Asia 1

Recipe 20 mg AI in 30 mg AI in 30 mg AI in 30 mg AI in one Tablet A one Tablet B one Tablet one Tablet

EurExp GenExp Production rate 40 000 tablets/h Nominal production time 10 h/week Overtime allowed 0 h/week Unavailabilitya 0 Downtime multipleb 0

aUnavailability is the probability of equipment breakdown based on historical data. bDowntime multiple represents how many times longer to process an order during the equipment breakdown or downtime.

Table 8 Details of the conversion processes for the intermediates in Europe Primary Manufacturing

Node Europe 1 Europe 2 Europe 3 Europe 4/5

Recipe 1 kg raw material 1 kg intermediate 1 1 kg intermediate 2 1 kg intermediate 3 1 kg intermediate 4 gives 1 kg gives 1 kg gives 1 kg gives 1 kg gives 1 kg Al

intermediate 1 intermediate 2 intermediate 3 intermediate 4 Production capacity 150 150 250 250 500 (kg/week) Unavailabilitya 0 0 0 0 0 Downtime multipleb 0 0 0 0 0

aUnavailability is the probability of equipment breakdown based on historical data. bDowntime multiple represents how many times longer to process an order during the equipment breakdown or downtime.

impact of quality control (QC) after production processes. The details of the cases are as follows:

Case (a): consistent and increasing under-forecast of Packs A and B such that

1/H t Dn,t = Dn,t +

- H ' 100

Case (b): consistent and increasing over-forecast of Packs A and B such that

1 H t Dn,t =

Dn,• Gjj20 j=1 2

Planning period Frozen Scheduling period period .

t = current time Time, t

Figure 7 Time period classification in the MRP control policy.

where t corresponds to the time step. For these two cases, we also investigate the effects of replacing the forecast dependent DRP policies with one of the ROP techniques, (s, Q), which is forecast independent. This can be easily done

810 Journal of the Operational Research Society Vol. 55, No. 8

Table 9 Comparison of the performance measures for various cases

Experiments Pack A (Japan) Pack C (USA)

CSL (%) PSO (%) INV (packs) CSL (%) PSO (%) INV (packs)

Base case 100 0.0 3.2 x 104 100 0.0 8.1 x 104 Case (a): consistently underforecast (DRP) 84 1.8 1.9 x 104 Same as base case Case (a): consistently underforecast (s, Q) 93 0.9 2.5 x 104 Same as base case Case (b): consistently overforecast (DRP) 100 0.0 4.3 x 104 Same as base case Case (b): consistently overforecast (s, Q) Same as base case Same as base case Case (c): QC considered Same as base case 88 6.4 7.7 x 104

with the object-oriented model. The safety stock point, s, is set to be the average of the safety stock points over the horizon in DRP, and the fixed order quantity, Q, is set to be 150% of the average forecast demand during the lead-time period.

Case (c): QC of 2 weeks after each intermediate production process within Primary Manufacturing and QC of 1 week after the tablet production process within Secondary Manufacturing.

In addition, the parameters of the replenishment control policies can be varied to examine their impact on the performance measures. As an example, we illustrate the results of the variation of the safety stock cover period for Pack A in the base case.

Results and discussions

The performance measures obtained for the final products, Packs A and C, are listed in Table 9 and displayed in Figures 8 to 16. It is found that applying LSS to the uncertain variables in descending order of importance halves the number of simulations required for the same accuracy compared to traditional MC.

For Case (a), in which Pack A is consistently under- forecast, the forecast-dependent DRP is shown to be unsatisfactory with merely an 84% customer service level, while the forecast-independent (s, Q) gives a better customer service level of 93%.

For the consistently over-forecast Case (b), the forecast dependent DRP keeps a 34% higher average inventory level, whereas the forecast-independent (s, Q) results in the same average inventory level as in the base case. These results show the necessity of switching replenishment control policy when the market gives a response different from the company's forecasts.

Case (c) considers the impact of QC on the supply chain performance. Owing to resource sharing and priority given to the Asian plant, the performance measures for Pack A are unaffected but those for Pack C suffer, with its customer service level lowered to 88%. This illustrates the undesirable impact resulting from lengthy QC processes, which needs to be overcome.

120000 ------ mean quantity

100000 - safety stock

95c0 upper confidence 80000 - 950o lower confidence

x 60000 - 0

< 40000 .

o. 20000

0 0 20 40 60 80 100

Time I weeks

Figure 8 Base case: Pack A mean stock level over the horizon.

400000

35~0000 mean quantity 350000 3 j

safety stock

m. 300000 - 950 upper confidence 950. lower confidence

Z 250000 -. . .

, 200000 -

o

?x 100000-

a. 50000

0 20 40 60 80 100 Time / weeks

Figure 9 Base case: Pack C mean on-hand stock level over the horizon.

Figures 14 to 16 show that the optimum safety stock cover for Pack A in the base case is 3 weeks instead of 4 weeks, as 100% customer service level and 0% probability of stock out are achieved with a 25% reduction of average inventory holding, which can significantly reduce the amount of working capital if Pack A is an expensive item.

In all, the above cases show the convenience offered by the object-oriented modelling approach that evaluation of different situations and decisions can be achieved easily

WY Hung et al-Dynamic modelling of supply chains 811

120000a - mean quantity

- 100000 -

.safety stock

-- - 95% upper confidence 95% lower confidence

80000

, 60000

40000 -

a. 20000

0 20 40 60 80 100 Time / weeks

Figure 10 Case (a) consistently under-forecast (DRP): Pack A mean on-hand stock level over the horizon.

120000 --- mean quantity

" 100000 - safety stock

o. - -- 95% upper confidence

95% lower confidence

- 80000

. >

60000- ,O

40000 -

. 20000 -

-YI:... .

0- 0 20 40 60 80 100

Time / weeks

Figure 11 Case (a) consistently under-forecast (s, Q): Pack A mean on-hand stock level over the horizon.

120000 1 -)- mean quantity

y 100000 safety stock o

.- 95% upper confidence

a. 95% lower confidence 80000 - --

CA- 60000 ----- - +

40000

a. 20000- - - - I -

0 20 40 60 80 100 Time / weeks

Figure 12 Case (b) consistently over-forecast (DRP): Pack A mean on-hand stock level over the horizon.

120000 --- mean quantity

.2 100000 safety stock o - -- 95% upper confidence

80000 95% lower confidence

60000 - - - - -

0 CO

. 20000+

0 20 40 60 80 100 Time / weeks

Figure 13 Case (b) consistently over-forecast (s, Q): Pack A mean on-hand stock level over the horizon.

98

S96

o 94

o 92

0 90

88 2 3 4 5

Safety stock cover for Pack A / weeks

Figure 14 Variation of customer service level against safety stock cover for Pack A.

1.8 1.6 1.4 1.2

1

%b 0.8 0.6

0 0.4 0.2

2 3 4 5 Safety stock cover for Pack A / weeks

Figure 15 Variation of probability of stock out against safety stock cover for Pack A.

with the reuse of code. It also allows the development of

dynamic operating decisions to suit the dynamic external

environment, such as switching between replenishment control policies when the demand deviation from forecasts

goes beyond a certain range.

812 Journal of the Operational Research Society Vol. 55, No. 8

45000

40000 c 35000

< 30000-

S25000 0 20000 z 15000

10000- 2 3 4 5 Safety stock cover for Pack A / weeks

Figure 16 Variation of average inventory against safety stock cover for Pack A.

Conclusions

As supply chain management becomes increasingly impor- tant for improving a firm's performance in today's dynamic and competitive business environment, it is beneficial to have a simulation model to explore and evaluate various supply chain improvement policies before their implementation. An object-oriented dynamic simulation model is developed for this purpose. The model developed is generic in that all kinds of supply chain nodes can be represented by specifying the information and physical systems it possesses and utilizes, as well as its decision-making policies. Then by connecting the modelled supply chain members together it can simulate a supply chain network.

The performance of the supply chain network is evaluated by dynamic stochastic simulation of how the members behave and react to discrete events, as in the real-life situations.

A case study has been considered to illustrate the applicability of the model developed. Work is underway to improve this model further by incorporating optimal produc- tion scheduling to give a more detailed production simulation.

Acknowledgements-We thank the Engineering and Physical Science Research Council (EPSRC) for the research studentship that provides financial support for this project.

Appendix

For the generic node in Figure 2, the associations among the components are described as follows:

o Both the Inbound and Outbound Material Manage- ment components contain a number of Inbound or Outbound SKU Replenishment units, each handling one type of SKU kept within the node.

o An Inbound SKU Replenishment unit for a certain type of material acts as a customer, while an Outbound SKU Replenishment unit for that type of material act as a supplier. Each customer-supplier relationship is modelled for one SKU.

o Each Inbound and Outbound SKU Replenishment unit contains a Control Policy to manage an SKU stockpile. The Control Policy can be any one of the techniques in Table 1 or a customized policy.

o There is an External Order Container for each customer-supplier pair for one type of SKU, which deals with the External Orders passing between the two nodes.

o An Outbound SKU Replenishment unit also issues Internal Orders to trigger material conversion.

o An Internal Order Container is thus maintained between an Outbound SKU Replenishment unit and the Material Conversion component within the same node.

o The Material Conversion component can be used to simulate production, packaging, or transportation. Its characteristics are

- to keep an Inventory that contains all the materials within the nodes, and has access to an individual SKU Stock via its SKU identity,

- to consume and produce a variety of SKU types, - to hold a number of Resources (eg equipment units,

human operators, utility) and a set of conversion Recipes, to sort the Internal Orders within the Internal Order Container before conversion according to a priority-sequencing rule that can be either EDD, FCFS, or a customized rule, and

- to give a conversion lead-time estimate for Internal Orders.

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Received 26 November 2002, accepted 9 February 2004