Mb0044 Unit 04 Slm

Production and Operations Management Unit 4

Sikkim Manipal University Page No. 68

Unit 4 Forecasting

Structure:

4.1 Introduction

Objectives

4.2 What is Forecasting?

4.3 The Strategic Importance of Forecasting

Human resources

Capacity

Supply chain management

4.4 Why Forecasting is required?

Benefits from forecasts

Cost implications of forecasting

Decision making using forecasting

4.5 Classification of Forecasting Process

4.6 Methods of Forecasting

4.7 Case-let

4.8 Forecasting and Product Life Cycle

4.9 Selection of the Forecasting Method

4.10 Qualitative Methods of Forecasting

4.11 Quantitative Methods

What is time series?

Naïve method

Moving average method

Weighted moving average

Exponential smoothing method

4.12 Associative Models of Forecasting

4.13 Accuracy of Forecasting

Mean Absolute Deviation (MAD)

Standard Error (SE) of estimate

4.14 Summary

4.15 Glossary

4.16 Terminal Questions

4.17 Answers

4.18 Case Study



Before we start forecasting, take a look at these famous quotes:

With over 50 foreign cars already on sale here, the Japanese auto industry

isn't likely to carve out a big slice of the U.S. market.

Business Week, 1958.

I think there is a world market for about five computers.

Thomas J. Watson, 1943, Chairman of the Board of IBM.

Do you want to forecast?

____________________________________________________________

4.1 Introduction

In the previous unit, we have dealt with the concepts of operations strategy,

competitive capabilities and core competencies, operations strategy as a

competitive weapon, linkage between corporate, business, and operations

strategy, developing operations strategy, elements or components of

operations strategy, competitive priorities, manufacturing strategies, service

strategies, and global strategies and role of operations strategy. In this unit,

we will deal with the concepts of forecasting, the strategic importance of

forecasting, why forecasting is required, classification of forecasting

process, methods of forecasting, forecasting and product life cycle, selection

of the forecasting method, qualitative and quantitative methods of

forecasting, associative models of forecasting, and accuracy of forecasting.

Every business activity aims to satisfy some needs and wants of the society

and hence tries to gauge the demand. Only when the demand is properly

understood and predicted with sufficient accuracy, it becomes possible to

develop and utilise the resources to cater to such demands. Thus, for any

business activity to be started, the first step would be to predict the demand

and then to develop the plans towards meeting the demand either partially

or fully. Hence, it is correctly said that forecasting the demand is the first

step and demand forecasting drives all the other activities of production

systems which include human resource planning, aggregate planning,

capacity planning, and scheduling. Even if a company decides to position

itself in a certain way, it has to have done forecasting. Thus good forecasts

are of critical importance in all aspects of a business.



The forecast is the only estimate of demand until the actual demand

becomes known. However, forecasts are seldom perfect because the

demand for a certain product or service is a complex function influenced by

a multitude of variables. Many of these variables are not controllable and

even not properly evaluated in terms of magnitude and frequency. This

means that outside factors which are not known to us or properly predicted

or controlled impact the forecast tremendously. Hence, it is essential to

allow for this reality. In other words, expecting an accurate forecast is self-

defeating.

Most forecasting techniques assume that there is some underlying stability

in the system, which is not the case always. Hence, product family and

aggregated forecasts are more accurate than individual product forecasts.

Objectives:

After studying this unit, you should be able to:

define forecasting

explain the importance of forecasting

explain when to use the qualitative models

apply the different methods of forecasting and compare the results

compute the measures of forecast accuracy

identify special cases like causal and seasonal models

use a tracking signal for checking the accuracy and efficiency of

forecasting

4.2 What Is Forecasting?

As stated in Heizer and Render (2010), forecasting is the art and science of

predicting the future events. Forecasting is an art because subjective

assessment coupled with historical and contemporary judgment is required

to improve the accuracy of forecasts. It is a science because a wide variety

of numerical methods are used to obtain a number or several numbers and

further analysed using mathematical models to ascertain the accuracy of

forecast.

In most of the cases, forecasting may involve taking historical data and

projecting them into the future with some sort of mathematical model. It may

be a subjective or an intuitive prediction. Many times, the forecasting may



even resemble a kind of a wild guess or may involve extensive data analysis

involving several parameters. Sometimes, it may involve a combination of a

mathematical model adjusted by a manager’s good judgment.

Forecasting is synonymous with estimating and prediction, though

forecasting is considered to be more scientific rather than a crude or vague

guesswork.

4.3 The Strategic Importance of Forecasting

Forecast is very much required for all types of industrial activity and also for

those industries which are purely in the service sector like healthcare and

education. Good forecasts are of critical importance in all aspects of a

business: The forecast is the only estimate of demand until the actual

demand becomes known. Therefore, forecast is said to drive decisions in

many business areas. Forecast influences three key activities. They are:

Human resources

Capacity

Supply chain management

Let us now discuss these three activities in detail.

4.3.1 Human resources

Typically, the number of persons required is a function of the production

output which, in turn, depends on demand forecasting. Hence hiring,

training, and laying off workers, all depend on the anticipated demand.

When fresh workers are hired anticipating a rise in the demand, it is

expected that they can quickly get into the required job. However, training is

required apart from developing good relations with the existing workers.

Similarly, if workers are removed, it sets a demoralising atmosphere.

Further, the removed workers will spread the news, and the industry will

suffer due to bad reputation and poor image.

4.3.2 Capacity

Capacity refers to the ability to meet the demand in terms of resources and

the preparedness on the part of the company. When the demand pattern is

well recognised and indicates a rise, the capacity build up happens and

ensures that there are no lost sales for want of product. On the other hand,

if the demand is showing a decline, it signals a decrease in capacity. Thus,



unnecessary investments are not made. Both for capacity-lead and

capacity-lag decisions, demand forecasting is vital.

4.3.3 Supply chain management

Supply chain management refers to all the activities that enable the right

product at the right place at the right price. Hence, demand forecasting has

to be done with utmost care to help identifying the vendors, pricing choices,

and material options. When the demand is properly forecasted, it is easy to

plan for the suppliers, logistics, and other intermediaries to ensure the

delivery of the product at the right time.

Self Assessment Questions

1. Forecasting is both art and science of predicting the future events.

(True/ False)

2. Demand forecasting is vital both for capacity-lead and capacity-lag

decisions. (True / False)

3. Forecasts are not always perfect because the demand for a certain

product or service is a complex function influenced by a multitude of

variables. (True / False)

4.4 Why Forecasting is required?

Forecasting is required for:

Production planning

Financial planning

Personnel planning

Scheduling planning

Facilities planning

Process design and planning

4.4.1 Benefits from forecasts

Forecasting basically helps to overcome the uncertainty about the demand

and thus provides a workable solution. Without the forecast, no production

function can be taken up. Hence, it can be stated that forecasting helps to:

Improve employee relations

Improve materials management

Get better use of capital and facilities

Improve customer service



4.4.2 Cost implications of forecasting

Forecasting requires special efforts and involves inputs from experts which

cost a lot to the companies. Well-trained experts and associations

substantially invest in human resources and hence charge their clients for

the service rendered. Thus, forecasting done in-house or carried out

externally requires significant investments. Thus, it can be said that more

the efforts put for forecasting, more will be the cost of forecasting. Because

of improved accuracy and better judgment, the losses that would occur

because of poor forecasting would decrease as more efforts are put in for

forecasting. Hence, higher the efforts, lower will be the losses. Because

effort is a direct function of forecasting, this cost goes up with increase in the

forecasting efforts. Figure 4.1 depicts the forecasting – cost implications

graphically.

Fig. 4.1: Forecasting – Cost Implications

From figure 4.1, it is to be understood that to keep the total cost of

forecasting to a minimum, it is necessary that the forecasting effort has to be

raised up to a level at which certain uncertainty is acceptable and hence,

there is preparedness for some possible loss. On the other hand, it doesn’t

make sense to increase the effort to improve the accuracy of forecasting

because the forecasts are subject to market dynamics and many other

unpredictable parameters which will not be known or controllable. For



example, the government’s import policy drastically affects the capacity and

thus any industry hoping of increasing the demand and expanding the

capacity will face a major threat and possible loss.

4.4.3 Decision making using forecasting

Forecasts are always subject to uncertainty because of the changing

environment and hence, any attempt to improve the forecast accuracy only

increases the cost but not the accuracy. Keeping this in mind, the

managerial decision makers adopt the following rule:

Actual decision = Decision assuming forecasting is correct + Allowance for

forecast error.

Further to account for the uncertainty and provide allowance, it is necessary

that the forecast output contains two numbers as follows:

1) Best estimate of the demand + 2) Error

Again the question, how much of error can creep in the forecast? It is

difficult to answer. However, the error in forecast is easy to calculate once

the actual demand is known.

Forecast error = Actual demand - Forecast demand

Figure 4.2 depicts the process of forecasting and the associated factors.

Fig. 4.2: Forecast Generation and Revision



What is being forecasted is called as the variable of interest

In the forecasting jargon, traditionally, it is assumed that it is the demand

that is always connected with sales. However in a general way, forecast

may refer to several things including the outcome of any process, naturally

occurring or created for a specific purpose. For example, election results,

material requirement, population, economic growth, weather, and even

tourists visiting a certain place.

Further, while forecasting, it helps to ask the following to improve the

accuracy of forecast:

Input elements involved

Process generating the variable

Availability of data

Stability of the process

Accuracy of data

Adequacy of data

Representativeness of the data

4.5 Classification of Forecasting Process

According to Heizer and Render (2008), the forecasting methods can be

classified based on the context or focus. The different forecasting methods

are discussed below.

Based on the type of database, the forecasting methods can be classified

into 2. They are:

Quantitative (Statistical forecasting)

Qualitative (Subjective estimation)

Based on the forecast time period, the forecasting methods can be

classified into 3. They are:

Short range – up to 1 year

Medium range – 1 to 3 years

Long range – 5 years or more

Based on the methodology, the forecasting methods can be classified into 3.

They are:

Time – series methods

Causal methods

Predictive methods (Qualitative methods)



Let us now discuss these methods in brief.

When forecasting for an existing product or similar to it, historical data will

be available and hence statistical methods can be applied. These include

simple time series models to very extensive methods like response surface

methodology. If no numerical data is available, then the opinion-based data

containing qualitative descriptions like good, bad, acceptable, etc will have

to be used. Also in some methods, the expert’s opinion or panel’s comments

will be used. Regarding the time horizon, it is obvious that some elements or

variables of interest will have to be predicted over long ranges like housing

development or global warming effects. In some cases, particularly for short

periods, some parameters like fuel prices, material availability, labour

availability, etc have to be predicted. Keeping these situations, several

methods of forecasting have been proposed and not all of them will be

relevant or useful under all situations. Thus, the decision maker has to make

a careful evaluation of all the choices before choosing the method.


4. Forecasting basically helps to overcome the ________ about the

demand and thus provides a workable solution.

5. Forecasting whether done in-house or carried out externally requires

significant investments. (True / False)

6. Forecast error = ___________ - Forecast demand.

4.6 Methods of Forecasting

The different methods of forecasting can be classified as follows:

Qualitative methods

Market surveys

Nominal group testing

Historical analysis

Jury of executive opinion

Life cycle analysis

Delphi method



Quantitative methods

Table 4.1: Quantitative methods classification

Time series analysis Causal methods

Moving averages

Exponential moving averages

Box – Jenkins method

Trend projections

Fourier series

Regression analysis

Input – output model

Leading indicators

Simulations model

Economic models

4.7 Case-let

Demand for Light Commercial Vehicles (LCV) in India

At present, Tata Motors dominates the market of LCV in India with a market

share of about 52% owing the success largely to their model, Tata Ace.

Mahindra group enjoys around 25% and the other players are Ashok

Leyland, Piaggio, and Eicher Motors.

The demand for LCVs is affected by rising interest rates, decreasing

industrial output, and a considerable increase in the vehicle prices. The

operating cost and environment too have changed significantly affecting the

sales.

In view of the decreasing demand, the manufacturers have to face the

challenge of reduced capacity utilisation. With freight rates almost stagnant,

the market seems to be dull in the short run. However, the long-term growth

holds promise as there will be economic changes. The LCV industry is

expected to grow by 17-18% in the financial year 2011-12. According to the

research conducted by J.D. Power Asia Pacific, India will be the third largest

LCV market by 2020. The report also says that given India’s poor road

infrastructure and concerns about fuel consumption, micro-van and mini

truck models in the LCV segment are likely to be popular.

(Source: Patel, J, LCV Industry – Begging to Differ, Business India, 4th

march

2012, page 30)



Discussion Questions:

a. What forecasting method might be suitable for the LCV segment?

b. How do you differentiate between poor growth in the short term and

promising growth in the long term?

4.8 Forecasting and Product Life Cycle

The demand for a product keeps changing as it passes through different

stages in its life cycle. The demand starts with zero value and keeps rising

as the product moves along the life cycle and gradually diminishes once the

product is outdated or obsolete. For example, iPad and iPhone are currently

in the growth stage and hence, the forecast can be trend based and on the

rise. But a product like a fixed telephone instrument is in the decline stage

and already being phased out. Hence, its forecast has to be carefully done

keeping in mind the decreasing sales. If methods are applied mechanically

without observing the current stage of the product, the forecast is bound to

be erroneous and leads to catastrophe. Figure 4.3 depicts the product life

cycle and volume of demand graphically.

Fig. 4.3: Product Life Cycle and Volume of Demand



Similarly, many of the web or internet-based transactions like online broking,

mail ordering, voice messaging, and online banking are witnessing a surge

in the demand and more people will start availing the service. In the banking

sector, the IT-enabled services are growing rapidly and hence have

decreased the demand for staff. Hence, when forecasting in such cases,

people need to understand the possible life left in the product and estimate

the demand. Further, there are also instances where the new product has

not gone through all the stages but became a failure after it was launched.

For example, pagers had a short life before giving way to mobile phones.

4.9 Selection of the Forecasting Method

Given the fact that several methods are available, the question is how to

select the right method for forecasting. Because cost, time, and skills are

involved, the choice of a forecasting method is based on several factors.

They are:

Form of forecast required

Forecast horizon, period, and interval

Data availability

Accuracy required

Behaviour of process being forecasted (demand pattern)

Cost of development, installation, and operation

Case of operation

Management comprehension and cooperation

4.10 Qualitative Methods of Forecasting

The different qualitative methods of forecasting are as follows:

Market surveys


Historical analysis


Life cycle analysis

Delphi method



Let us now discuss these qualitative methods in detail.

Market surveys

Conducting surveys among the prospective buyers or users is a very old

method of forecasting. Here, a questionnaire is prepared and circulated

among the people and their responses are obtained. The responses are

collated and analysed to reveal possible clues towards acceptance or

otherwise about a new product or service. Based on the overall decision, the

forecasting is done. This method is typically done for new products or at

new places where a product is to be launched. In this method, the number

of respondents and how responses are gathered like through oral

interviews, personal talks, internet based, postal ballots, etc, have to be

established before survey. The common limitations are the sample size and

the way of drawing the sample like random, convenient, or judgmental.

Sample bias is not completely ruled out.


In the nominal group testing method, the product or service may be given a

trial use to a specified group like students, employees, neighbors, etc and

their responses are collected and analysed.

Historical analysis

The historical analysis method is based on the fact that the past is an

indicator of the future. People try to associate the events that happened

earlier with the events that are likely to happen in the future.


In the jury of executive opinion method, the opinion of a group of experts is

collected and used as an estimate to obtain the forecast.

Life cycle analysis

In the life cycle analysis method, an assessment of the life cycle stage in

which the product lies is made first and an opinion is formed.

Delphi method

In the Delphi method, the experts give their opinions which are collected by

the coordinator and several rounds of discussion may be held before a

consensus is reached. This forms the basis for forecasting.



4.11 Quantitative Methods

Under the quantitative methods, adequate data is collected and different

statistical techniques are applied to reveal some patterns which will serve as

forecast. Because these methods heavily rely upon the data, it is essential

that the collected data is free from errors and bias so that proper

conclusions can be made. Another advantage is the availability of several

softwares including MS Excel which help to analyse the data extensively

which makes these methods easy to learn and apply.

The quantitative methods are divided into two groups. They are time series

analysis and causal methods.

Table 4.2: Classification of Quantitative methods

Time series analysis Causal methods

Moving averages

Exponential moving averages

Box – Jenkins method

Trend projections

Fourier series

Regression analysis

Input – output model

Leading indicators

Simulations model

Economic models

In the time series methods, one set of data or several sets are analysed to

obtain the forecast. In the causal methods, the association between two

variables forms the basis for forecasting.

4.11.1 What is a time series?

A time series is defined as a set of values pertaining to a variable collected

at regular intervals (weekly, quarterly, or yearly). For example, the

temperature recorded every one hour is time series. Similarly, the annual

rainfall or agricultural output forms a time series. However, it is to be noted

that to draw a reasonable conclusion, at least observations should be

available. With very little number of values, say 7 or 8, the forecasts will not

be accurate.

A time series consists of four components namely:

1) Trend

2) Cyclic

3) Seasonality

4) Random



Let us now discuss these components in brief.

Trend refers to the gradual upward or downward movement of data over a

long period of time. Cycles are repetitions of data in a certain pattern at

regular intervals like several years. Business cycles are very commonly

used to understand the mood of the markets. Seasonal pattern is also a

repetitive pattern but observed at much lesser frequency. The season length

could be every hour in a day, a day, a week, or months. Variations are

noticed at each time period and patterns are observed. Random variations

are difficult to predict and are caused by chance factors or unusual events.

For example, tsunami wrecked the tourist inflow at several popular holiday

destinations all over the world. Figure 4.4 depicts the four components of a

time series.

Fig. 4.4: Components of a Time Series

4.11.2 Naïve method

In the naive method, a set of observations pertaining to a certain variable

like sales, production, or consumption is observed and the forecast is taken

as the same value as that of the most recent period.



For example, as stated in www.icra.in the number of small car offerings is

given in the table 4.3 below.

Table 4.3: Number of small car offerings

1 2 3 4 5 6 7

Year 2007 2008 2009 2010 2011 2012 2013

Number of small

car offerings 9 14 17 23 26 31 35

The forecast as given by ICRA is 35 for the year 2013.

Fig. 4.5: Graph showing number of small car offerings

Using the naïve method, the forecast for the year 2013 is 31.

4.11.3 Moving average method

A moving average is obtained by summing and averaging the values of a

time series over a given number of periods repetitively, each time deleting

the oldest value and adding a new value. Usually, the number of time

periods chosen will be an odd number like 3 or 5 or 7. Rarely, there will be a

need to go beyond 7 periods.

Consider the same example as given before.

The three-year moving average for the first three periods = (9+14+17)/3 =

13.33



Every time an old period data is dropped and the new period data is

included to get the average. Therefore, the next three-year moving average

= (14+17+23)/3 = 18

This calculation is continued.

Similarly, the five-year moving average for the first five periods =

(9+14+17+23+26)/5 = 17.8

The next five-year moving average = (14+17+23+26+31)/5 = 22.2

Table 4.4: Moving averages

1 2 3 4 5 6 7

Year 2007 2008 2009 2010 2011 2012 2013

Number of small

car offerings 9 14 17 23 26 31 35

Moving average

3 periods 13.333 18 22 26.667 30.667

Moving average

5 periods 17.8 22.2 26.4

To decide upon the number of time periods, the following guide line may be

used:

(AP = Averaging Period)

Table 4.5: Guide line

Noise Dampening

Ability Impulse Response Accuracy

AP = 3 Low High Low

AP = 5 Medium Medium High

AP = 7 High Low Medium

Noise dampening refers to the ability to smooth out the variations. Impulse

response enables to detect immediate changes and accuracy implies

minimum forecast error.

Drawbacks of moving average methods:

All the past periods in the averaging period are weighted equally

No provision is made for seasonal patterns



Several periods of historical data must be carried forward from period to

period for calculating the forecasts

4.11.4 Weighted moving average

In the simple moving average, all the past periods in the averaging period

are weighted equally and hence, the forecast is sometimes influenced by

bigger values. Secondly, older values are not relevant, particularly in the

changing environments. Hence, to reflect those changes, the simple moving

average method is modified by using different weights to different time

periods. A weighted average generally gives more weight to recent

observations than older ones. This has an advantage over simple moving

averages that, older values are given less importance than more recent

values of a series and that the number of values included in the average can

be large while still achieving responsiveness to changes through judicious

selection of weights. However, the choice of weights is somewhat arbitrary

and is often based on trial and error approach.

For example consider the following data:

Table 4.6: Data showing the sales for six months

Month Sales in lakhs of

Rupees

Jan 90

Feb 70

Mar 80

Apr 85

May 82

June ?

Simple moving average (4 months average)

Forecast for the month of June = ¼ [70+80+85+82] = 79.25 lakh of Rupees

Here the weights are = 1/4 for all the values.

Weighted moving average (Using weights 0.1, 0.2, 0.3, 0.4)

Forecast for the month of June

= 0.1 X 70 + 0.2 X 80 + 0.3 X 85 + 0.4 X 82 = 81.3 lakh of rupees

This simple modification to the moving average method allows forecasters

to specify the relative importance of past periods of data.



4.11.5 Exponential smoothing method

This method is a modified weighted moving average method using weights

in an exponentially increasing way. The name exponential smoothing is

derived from the way the weights are assigned to historical data: The most

recent values receive most of the weight and weights decrease

exponentially as we go back in the periods.

Each new forecast is based on the previous forecast plus a percentage of

the difference between that forecast and the actual value of the series at

that point.

New forecast = Old forecast + α [Actual value - old forecast value]

Where α = a percentage and (actual – old forecast) = an error

Mathematically,

Ft =Ft-1 + α (At –1 –Ft-1)

Where Ft = Forecast for the period t

Ft-1 = forecast for the period (t-1)

α = Smoothing constant, varying from 0 to 1

At-1 = Actual value for the period (t-1)

Typically values of α range from 0.01 to 0.50. Higher values of α respond

more rapidly to any discrepancies, i.e., the changes in time series are more

closely tracked by higher values of α.

One important limitation of simple exponential smoothing is that it is ill–

suited for data that includes long-term upward or downward movements (i.e.

trend). Use of simple exponential smoothing in such instances would

produce forecasts that are too low for upward movements and too high for

downward movements. Therefore, when trend is present in time series data,

simple exponential smoothing should not be used, instead, exponential

smoothing adjusted for trend should be used.

Exponentially weighted moving averages is the term used for exponential

smoothing.

Sometimes α is calculated as 2/(AP +1), where AP = Averaging Periods

Exponential smoothing methods have been further extended to include

other possible variations and two such methods are:

1. Double Smoothing 2. Box – Jenkins methods

These methods are beyond the scope of the present topic.




7. Forecasting is broadly classified as __________ and _____________.

8. Delphi method is a _________ method of forecasting.

9. A _________ is defined as a set of values pertaining to a variable

collected at regular intervals (weekly, quarterly, or yearly).

10. The ________ method of forecasting is based on the fact that the past

is an indicator of the future

4.12 Associative Models of Forecasting

The methods earlier discussed analysed the data pertaining to a single

variable and applying statistical methods developed the forecast. But in

industries, it has been observed that there are many situations where the

data values of one variable have some association with the data values of

another variable. Though this is not exactly a cause and effect situation, it is

possible to find out the extent of association and hence, when one variable’s

value is known, the value of the other variable can be estimated using the

mathematical relationship. Correlation and regression analyses are

commonly used to establish such relationships and also help to obtain the

forecast.

Regression and correlation techniques are means of describing the

association between two or more such variables. Regression means

“dependence” and correlation measures the degree of dependence. Using

the regression equation, it is possible to estimate the value of a ‘dependent’

variable, Y, from an ‘independent‘ variable, X.

Two types of regressions are possible:

a) Simple regression involves only one independent variable which affects

the dependent variable. For example, the gold price is influenced by,

say, rising income.

b) Multiple regressions involve two or more independent variables

influencing the dependent variable. For example, the real estate price is

influenced by rising income, shortage of land, and urban migration.

Regression is also categorised as linear and non–linear regression based

on the severity of relationship and characteristics. The following table 4.7

shows the examples.



Table 4.7: Linear and non–linear regression

Simple Multiple

Linear Y= a +b x Y=a+bx1+cx2+dx3

Non-linear Y= a+bx2 Y=A+BX1+CX22+DX3

3

It is to be remembered that known variable = Independent variable and

unknown variable = Dependent variable.

The forecasting procedures using regression involves the following steps:

1. The variables are plotted along Cartesian or rectangular coordinates

2. A trend equation is developed

3. The equation is used for forecasting

4. The variables are not necessarily related on a time basis

The most popular form of the simple linear regression equation is Y = a+bX,

where

Y= Dependent variable

X= Independent variable

a = Y intercept

b = Slope

For a unit change in the value of X, a change in the value of Y occurs in a

straight line manner and hence, it is easy to predict the values.

To find the values of constants a and b, the following equations are used:

∑y = na + b∑x

∑xy = a ∑x +b∑x2

Solving the above two equations, the values of a and b are obtained and

then substituted into the regression equation along with the value of X and

the value of Y is determined.

Example:

A departmental store has collected data about sales figures and profits

during the last 12 months. Obtain a regression line for the data and predict

the profit when sale is 10 Rs. lakh.



Table 4.8: Data on sales

Sales X

(Rs. Lakh): 7 2 6 4 14 15 16 12 14 20 15 7

Profit Y

(Rs.

thousands)

15 10 13 15 25 27 24 20 27 44 24 17

First plot the data and decide if a linear model is reasonable (i.e. do the

points seem to scatter around a straight line?) Next compute the quantities

∑x, ∑y, ∑xy and ∑x2.

Let linear regression equation is Y = a+bX, where

Y= Dependent variable, profit

X= Independent variable, sales

a = Y intercept

b = Slope

The following table is constructed:

Table 4.9: Table Construction for regression

X Y XY X2 Y

2 Ŷ

7 15 105 49 225 16.15

2 10 20 4 100 8.186

6 13 78 36 169 14.558

4 15 60 16 225 11.372

14 25 350 196 625 27.302

15 27 405 225 729 28.895

16 24 384 256 576 30.488

12 20 240 144 400 24.116

14 27 378 196 729 27.302

20 44 880 400 1936 36.86

15 34 510 225 1156 28.895

7 17 119 49 289 16.15

Total ∑ 132 271 3529 1796 7159

Solving for a and b, we get a = 5.06 and b = 1.593

Therefore, the regression line is

Y = 5.06 + 1.593 x

When sales X=10,

Y = 5.06 +1.593 X = 20.99 Rs. Thousands



Self Practice Problem

Maxwell Motors has collected the following data on annual spare parts sales

and new car registrations:

Table 4.10: Data on annual spare parts

Annual spare parts sales

(in million $)

1.0 1.4 1.9 2.0 1.8 2.1 2.3

New car registrations (in

thousands)

10 12 15 16 14 17 20

Develop the linear regression equation and estimate the spare parts sales

when new car registrations are 22,000.

Answer:

Linear Regression equation:

Y = -0.16 + 0.13 X

Spare parts sales when new car registrations are 22,000 = 2.7 million $

4.13 Accuracy of Forecasting

Finally, we come to an important question. How accurate are the forecasts

obtained by the different methods. Any forecast method results in values

that may not exactly match the actual values. Hence, deviations are

expected. Higher the deviation, more will be the error. Several measures of

error in forecast have been developed to examine the issue of error in

forecast. Here, we look at two widely used and popular measure applicable

to a wide variety of methods. These two measures are: (1) Mean Absolute

Deviation (MAD), and (2) Standard Error of Estimate (SE).

4.13.1 Mean Absolute Deviation (MAD)

In short range forecasting, MAD is often used to measure how closely

forecast values are matching the actual data. MAD is computed as follows:

MAD = Sum of absolute deviations for n periods / number of periods.

Here deviation = Difference between the actual value and the forecast

value.

These deviations are added and divided by the number of time periods to

get the MAD.



4.13.2 Standard Error (SE) of estimate

The standard error of estimate measures the variability or scatter of the

observed values around the regression line.

The formula for calculating SE is given below:

where

y = values of the dependent variable

yest = Estimated values from the estimating equation that correspond to each

Y value.

n = number of data points used to fit the regression line.

It is important to note that the error values should be as low as possible

while making comparison and selection.

4.14 Summary

Let us now summarise the key learnings of this unit:

For any business activity to be started, the first step would be to predict

the demand and then to develop the plans towards meeting the demand

either partially or fully. This process of estimating is called forecasting

Forecasting basically helps to overcome the uncertainty about the

demand and thus provides a workable solution.

Supply chain management refers to all the activities that enable the right

product at the right place at the right price. Hence, demand forecasting

has to be done with utmost care to help identifying the vendors, pricing

choices, and material options.

Forecasting is broadly classified as quantitative and qualitative

Market survey, Delphi method, historical analysis are some of the

qualitative methods of forecasting

The quantitative methods are divided into two groups. They are time

series analysis and causal methods.



Several measures of error in forecast have been developed to examine

the issue of error in forecast. There are two widely used and popular

measure applicable to a wide variety of methods. These two measures

are: (1) Mean Absolute Deviation and (2) Standard Error of Estimate.

4.15 Glossary

Survey: A detailed study of a market or geographical area to gather

data on demand for a product or service, attitudes, opinions, satisfaction

level, etc

Questionnaire: A form containing a set of questions submitted to

people to gain statistical information

4.16 Terminal Questions

1. What is meant by forecasting?

2. Discuss the role of forecasting in modern business context.

3. List the benefits of forecasting.

4. Distinguish between moving average method and weighted moving

average method. What are the advantages and disadvantages of these

methods?

5. How do you measure the accuracy of forecast? Describe one measure

of error used in forecasting.

4.17 Answers


1. True

2. True

3. True

4. Uncertainty

5. True

6. Actual demand

7. quantitative, qualitative

8. qualitative

9. time series

10. historical analysis



Terminal Questions

1. Refer to section 4.2

2. Refer to section 4.3 and 4.4

3. Refer to section 4.4.1



4.18 Case Study

Plastic Junction – The Road Ahead

Today, it may not be an overstatement to say that we are living in a plastic

world. With metal and wood, which were the most commonly used materials

for all types of products for centuries, now being replaced by plastic; we

cannot imagine life without plastic. You name the product, it is there: bottles,

door, furniture, credit card, containers, auto parts, and the list go on. These

growing applications of plastic are very encouraging to the plastic

manufacturers world over, and the Indian manufacturers are no exception.

Plastic manufacturing in India made a humble beginning in India in 1957

when the commercial production of polystyrene started. This was followed

by production of LDPE (Low Density Poly Ethylene) in 1959, PVC (poly

Vinyl Chloride) in 1961, HDPE (High Density Poly Ethylene) in 1968, and

polypropylene in 1978.

Indian plastic manufacturing industry largely consists of small and medium

enterprises numbering over 30,000 and in the post-liberalisation era after

1991 saw a spurt in joint ventures, foreign investments, and technology

acquisitions. This has created a tremendous capacity even in excess of

demand in certain segments. With even big industries starting their units

related to plastic products manufacturing, the overall industry growth has

been quite encouraging.

As stated by Yogesh Shaw, President of All India Plastic Manufacturers’

Association, plastics is a Rs. 85,000 crore turnover industry in India,

employing directly and indirectly 3.5 million people and yielding revenues of

Rs. 7300 crore to the government annually. He projects plastic production to

increase by 60% to reach 12.75 million tones by 2012. It is also expected

that the per capita consumption of plastic will double up from the present



eight kg in the next five years. In comparison, China is 17 kg, US and

Europe well over 80 kg, and the world average 23 kg.

The plastic production is boosted by the increase in the availability of raw

material which comes from petrochemicals industry because of the capacity

additions. A yearly growth of 15% is expected to continue for some more

time.

The major threat to the Indian plastic industry is from China which exports

huge quantity of plastic to many countries including India. With cost of

acquisition low, Indian promoters also favour using China plastic. In the

recent times, the environment consciousness among the people is

pressurising the government and the industries to reduce the consumption

of plastic and also not to promote the plastic industry. Some major changes

too have been brought in by the ruling governments to curb the use of

plastic. “Plastic Free Zone” is the new sign board people have to watch.

(Source: Bana, S. (2011). “It’s a plastic world”, Business India, August 21, 2011, pp

106-108)

Discussion Questions:

1. Which model of forecasting do you suggest for plastic industry?

2. How do you factor in the Chinese threat and the environmental issues in

the growth of the industry?

3. If you are a manager in the plastic manufacturing industry, how do you

react to the positive and negative factors to the growth of the industry?

Reference:

Heizer, J. H. and Render, B. (2008), Operations Management, Flexible

Version, Pearson Prentice Hall, 2008.

Bana, S. (2011). “It’s a plastic world”, Business India, August 21, 2011,

pp 106-108

E-Reference:

www.icra.in

saber.uca.edu

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