Forecasting of Demand for Production Planning and Control

Production Planning and Control: Forecasting Techniques
Qualitative and Quantitative Tools
Time Series Analysis

Production Planning and Control: Forecasting Techniques, Qualitative and Quantitative Tools, and Time Series Analysis

Introduction

Production planning and control (PPC) is an essential component of manufacturing and operations management. It is designed to ensure that production processes operate efficiently and meet the demands of the market while minimizing waste, reducing costs, and optimizing resources. The core of PPC is forecasting, as it enables organizations to predict future demand and make informed decisions regarding inventory management, production scheduling, and resource allocation. Accurate forecasting helps businesses respond to changes in market demand, manage supply chain processes, and ensure customer satisfaction.

Forecasting techniques can be broadly classified into qualitative and quantitative methods. Qualitative tools rely on subjective judgment and expert opinion, making them ideal for situations where historical data is unavailable or where uncertainty is high. In contrast, quantitative tools depend on numerical data and statistical models to generate forecasts, often using past data to project future trends. One of the most commonly used quantitative methods is time series analysis, which examines historical data to identify patterns and predict future outcomes.

This essay will explore forecasting techniques in PPC, focusing on qualitative and quantitative tools and delving into the intricacies of time series analysis. We will examine their importance, applications, and the various models used to improve production efficiency and meet customer demands.

1. Production Planning and Control: An Overview

Production planning and control (PPC) is the process of organizing, directing, and controlling production activities to ensure that goods and services are produced at the right time, in the right quantity, and at the right quality level. The goal of PPC is to optimize production efficiency, minimize waste, and maximize customer satisfaction by ensuring that production processes align with demand.

1.1 The Role of Forecasting in PPC

Forecasting is the backbone of PPC. Accurate forecasts allow businesses to plan for the future, allocate resources efficiently, and make informed decisions about production schedules, inventory levels, and capacity requirements. Without effective forecasting, companies risk overproducing or underproducing, leading to inventory surpluses or stockouts, respectively. This can result in increased costs, reduced customer satisfaction, and lost revenue.

Forecasting in PPC is used to predict various factors, such as:

Demand forecasting: Estimating the future demand for products to plan production schedules and inventory levels

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Production
Planning and
Control
MP9080

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Forecasting

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Forecasting
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•Forecasting is a management technique to estimate the sales of a product or service in physical units for a
fixed future period, under the proposed or existing market plan.
•It assumes a set of economic and other forces outside the organization for which the forecast is made. It
determines how to allocate their budgets for an upcoming period of time.
•It also provides an important benchmark for firms to determine their future operations, policy planning, and
reengineering if necessary.
•The dynamic changes in the quantity or quality of products and/or services require a change in the
organization structure.

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The need for forecasting
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•All organizations operate in an atmosphere of uncertainty. Due to the rapid changes in technology, an organization’s involvement in the
national scenario of the economic, social, and political changes depends very significantly on the forecasting of not only their sales but
also the other forces effecting their operations.
•It is essential to obtain an estimate of the changes as accurately as possible for companies to survive and to strive for operational
excellence. This necessitates the need for companies to develop reliable forecasting systems.
1.Most industrial activities depend upon future sales because no sales means no production.
2.Forecasting plays an important role for the development of future plans.
3.Forecasting is used for decision-making investments in plants.
4.It is used for planning marketing strategy and programming.
5.Scheduling of production activities depends on forecasting.
6.Forecasting is needed for effective manpower planning.
7.Forecasting facilitates planning for effective utilization of the plant and machinery.
8.Forecasting is used for material planning and replenishment action (making available the right material at the right time in the right quantities).
9.Forecasting provides information on the relationship between the demands for different products.
10.Forecasting is used for product design and development.
11.Forecasting helps company expansions and diversification.

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Demand Management
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•The purpose of demand management is to coordinate and control all sources of demand so the supply
chain can be run efficiently, and the product delivered on time.
•Where does demand for a firm’s product or service come from, and what can a firm do to manage it?
There are two basic sources of demand: dependent demand and independent demand.
•Dependent demand is the demand for a product or service caused by the demand for other products or
services. For example, if a firm sells 1,000 tricycles, then 1,000 front wheels and 2,000 rear wheels are
needed. This type of internal demand needs not a forecast, just a tabulation.
•As to how many tricycles the firm might sell, this is called independent demand because its demand
cannot be derived directly from that of other products. There is not much a firm can do about dependent
demand. It must be met (although the product or service can be purchased rather than produced
internally).

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Independent demand and firm
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•Take an active role to influence demand: The firm can apply pressure on its sales force, it can offer
incentives both to customers and to its own personnel, it can wage campaigns to sell products, and it can
cut prices. These actions can increase demand. Conversely, demand can be decreased through price
increases or reduced sales efforts.
•Take a passive role and simply respond to demand: There are several reasons a firm may not try to
change demand but simply accept what happens. If a firm is running at full capacity, it may not want to do
anything about demand. Other reasons are a firm may be powerless to change demand because of the
expense to advertise; the market may be fixed in size and static; or demand is beyond its control (such as
in the case of sole supplier). There are other competitive, legal, environmental, ethical, and moral reasons
that market demand is passively accepted.

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Basic steps of forecasting
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1.Identify and determine the objectives, the purpose, and need for the forecast.
2.Establish a time horizon.
3.Categorize the products.
4.Select a forecasting technique.
5.Identify and select the definite variables that affect the demand.
6.Gather and analyze data.
7.Make the forecast.
8.Make trend correction, etc., where relevant.
9.Monitor the forecast.

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Characteristics of a good forecast
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1.Accurate—Some degree of accuracy should be determined to make a comparison with other alternative
forecasts.
2.Reliable—The user should establish some degree of confidence.
3.Timely—It is necessary to set a certain amount of time in response to make changes if necessary.
4.Easy to use and understand—Users should find the forecast comfortable to work with.
5.Cost-effective—The cost should not be higher than the benefits obtained from the forecast.

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Short-term, medium-term, and long-term forecasts
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•Forecasting is an integral part of the decision-making activities of management, as it plays an important
role in many areas of a company. Modern organizations require short-term, medium-term, and long-term
forecasts, depending on the specific application.
•Short-term forecasts (up to 1 year) are needed for the scheduling of personnel, production, and
transportation. As part of the scheduling process, forecasts of demand are also required.
•Medium-term forecasts (up to 5 years) are needed to determine future resource requirements in order to
purchase raw materials, hire personnel, or buy machinery and equipment.
•Long-term forecasts (over 5 years) are used in strategic planning. Such decisions must take account of
market opportunities, environmental factors, and internal resources.

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Techniques of forecasting
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Qualitative forecasting methods
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•Qualitative forecasting methods are based on the opinion and judgment of consumers and field-wise
experts. These techniques are subjective and used when all required data is not available. Intermediate- or
long-range decisions can be made, but not short-range or immediate decisions, like shop floor planning.
The following are some of the qualitative forecasting methods,
1. Opinion survey
2. Customer and distributor survey
3. Aided judgment
4. Judgmental bootstrapping
5. Jury of executive opinion
6. Delphi technique
7. Prediction markets
8. Marketing trials
9. Market research
10. Simulated interaction

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Qualitative or judgmental forecasting methods
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•Opinion survey: Pre-poll and exit surveys are used when the media conducts surveys among the public
chosen at random to get their opinions about who will win and how many votes they may get in an election.
This principle can be applied to businesses conducting similar surveys among the public about specific
marketing aspects of certain products. Opinions are collected from prospective buyers on what they buy
and why they want to buy certain products. The statistical principle of sampling makes it possible to
estimate how the general population would respond to the product. This is relatively simple and is the most
commonly adapted method used by startups. This method is sometimes referred to as intentions and
expectations surveys.
•Aided judgment: When a startup company in a new industry lacks data about the market, aided judgment,
based on feedback from potential customers, experienced sales staff, and industry experts, can either be
aided by using only intuition and personal judgment or aided by more specific analysis of the available
information, depending upon the situation. Comparing the fuel economy data of a certain model car with
those of other models of the same make as well as those of other makes and models of similar-sized
engines is an example of this.

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Qualitative or judgmental forecasting methods
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•Judgmental bootstrapping: The term bootstrapping originated in the early 19th century in the United
States, and it usually refers to a self-starting process that is supposed to proceed without external input. In
business, it refers to starting a business without external help or capital. Here the entrepreneur makes the
decisions by himself, in a manner similar to unaided judgment. A majority of the startups that are now
started by young entrepreneurs, who use their judgement and intuition in deciding their business activities,
fall under this category.
•Jury of executive opinion: NASDAQ (National Association of Securities Dealers Automated Quotations)
defines jury of executive opinion as a method of forecasting using a composite forecast prepared by a
number of individual experts. The experts form their own opinions initially from the data given and then
revise their opinions according to others’ opinions. Finally, each independent jury’s final opinions are listed,
analyzed, and combined. Business Dictionary gives a more elaborate explanatory definition to the concept
of jury of executive opinion as a method of integrating, combining, and averaging views of several
executives regarding a specific decision or forecast. The general practice is to bring together top
executives from finance, resources, marketing, purchasing, and production, etc., who provide their
background information, experiences, and opinions to the board of directors. This exercise usually leads to
a quicker (and often more reliable) result without the use of elaborate data manipulation and other
statistical tools and techniques, where applicable.

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Qualitative or judgmental forecasting methods
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•Delphi technique: Delphi technique, whose name is derived from the Oracle of Delphi, is based on the
principle that forecasts from a structured group of individuals are more accurate than those from
unstructured groups, and that group judgments are more valid than individual judgments. A panel of
experts answer prepared questionnaires in two or more rounds. After each round, these anonymous
answers together with the reasons offered by them for their forecasts are summarized and given to the
experts, who revise their earlier estimates in light of those of other members of the panel, and give more
logical, more accurate figures. This is similar to the jury of executive opinion method, except that the
experts answer the questions individually in two or three rounds.
•Prediction markets: Prediction markets are speculations made for the purpose of making predictions of
future demands. Prediction of market prices generally is close to the mean belief of market participants.
This forecasting is generally adapted for the share market and pre-poll election results. The fluctuation of
the market prices can indicate what the public thinks of the probability of the item and consequently the
fluctuations in the probable sales of the item.

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Qualitative or judgmental forecasting methods
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•Marketing trials: If a product is absolutely new to the market, it is difficult to know the customers’
acceptability of the product since past data is not available. In such cases, the product is produced first as
a trial batch and is sent to the market for actual trial, with requisite advertisement, promotion, etc., and then
depending upon its success during the pilot trial, further batches are released. This method is normally
followed for items like cosmetics and toothpaste.
•Market research: Before releasing new products into the market, organizations conduct market research to
collect required data and conduct surveys for information on factors that influence the product demand, like
location, demography, nature of the consumption, buyer perception, buyer income levels, acceptable price
structure, etc. The data collection and analysis may comprise one or more of the methods previously
detailed and would be more target-oriented. This method can also take advantage of specialist consultants
in the field of market research, who have the specified experience and large databanks.
•Simulated interaction: Simulated interaction in forecasting is similar to the decisions that people will make
in conflict situations such as buyer-seller negotiations, employer union disputes, commercial competition,
hostile takeover bids, civil unrest, international trade negotiations, etc. The primary reason simulated
interaction works is that it gets a person to think like the other party. That is, it puts them in the other
person’s shoes.

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Quantitative forecasting techniques
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•Discrete event simulation: Discrete event simulation (DES) is the process of codifying the behavior of a
complex system as an ordered sequence of well-defined events. Each event occurs at a particular instant
in time and marks a change of state in the system. This is basically used to monitor and predict the
behavior of investments like the stock market, but this tool is now increasingly used to predict the market
for industrial goods.
•Group method of data handling: GMDH is a family of inductive algorithms for computer-based
mathematical modeling of multiparametric datasets that features fully automatic structural and parametric
optimization of models. It is now increasingly applied for data mining and knowledge discovery in
forecasting. Using a computer aims to minimize the influence of the forecaster on the modeling.
•Reference class forecasting: Reference class forecasting, or comparison class forecasting, is the method
of predicting the future through looking at similar past situations and their outcomes. It involves the
following three steps:
1.Identify a reference class of past, similar projects.
2.Establish a probability distribution for the selected reference class for the parameter that is being forecast.
3.Compare the specific project with the reference class distribution in order to establish the most likely outcome for
the specific project.

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Quantitative forecasting techniques
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•Quantitative analogies: Quantitative analogy is a forecasting method that assumes that two different kinds
of phenomena share the same model of behavior. For example, one way to predict the sales of a new
product is to choose an existing product that is similar to the new product in terms of the expected demand
pattern for the product sales. Qualitative analogies are suitable for sketch understanding systems because
they highlight important relationships while leaving out details that are nonessential for conceptual
understanding.
•Game theory: Game theory, also called interactive decision theory, is the study of strategic decision-
making by creating mathematical models of conflict and cooperation among intelligent rational decision-
makers. Developed during the 1950s, it was originally used in economics, political science, and
psychology but has now become an umbrella term for the science of logical decision-making in business.

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Quantitative forecasting techniques
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•Data mining: Data mining is an analytic process designed to explore large amounts of business or market-
related data to identify consistent patterns and systematic relationships among variables and then to
validate the findings by applying the detected patterns to new subsets of data. This is performed in three
stages:
1.The initial exploration, which includes data preparation, data transformations, and selection of subsets in data
2.Model building or pattern identification with validation/verification for competitive evaluation of models
3.Using the model selected as best in the previous stage and applying it to new data in order to generate
predictions or estimates of the expected outcome
•Conjoint analysis: Originated by Paul Green and V. Srinivasan of Stanford University from mathematical
psychology, conjoint analysis is a statistical technique used in market research to determine how people
value different attributes (feature, function, benefits) that make up an individual product or service. It
determines which combination of a limited number of attributes influences the respondent’s choice or
decision-making. It is also used in testing customer acceptance of new product designs or the appeal of
advertisements to the customers and also in-service design.

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Quantitative forecasting techniques
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Causal models:
•Business Dictionary defines forecasting as estimating the cause-and-effect relationship based on the
assumption that the variable to be forecast (dependent variable) has a cause-and-effect relationship with
one or more other (independent) variables. In other words, the information available in the value of one
variable enables us to forecast the value of another variable.
•For example, information about temperature variations would help us to forecast the sales of electric fans,
or some information about the international cricket match series would help us to forecast the sale of T-
shirts and similar sports goods.
•Several informal methods used in causal forecasting use the judgment of the forecaster. Some forecasts
take account of past relationships among variables. If one variable has, for example, been approximately
linearly related to another for a long period of time, it may be appropriate to extrapolate such a relationship
into the future.

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Causal models
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The causal methods can either be by regressive or autoregressive analysis:
• Regression analysis includes a large group of methods for predicting future values of a variable using
information about other variables. These methods include both parametric (linear or nonlinear) and
nonparametric techniques.
• Autoregressive moving average with exogenous inputs (ARMAX). Quantitative forecasting models are
often judged against each other by comparing their in-sample or out-of-sample mean square error,
although some researchers have advised against this.

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Quantitative forecasting techniques
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•Segmentation: As the name implies, segmentation classifies the customers into A, B, or C groups
according to their buying pattern and then analyzes them based on the group or the segment. This is
somewhat similar to the A, B, and C grouping of inventory items or the classic 80-20 rule of the economic
segmentation of the general population. Segmentation is essentially the identification of subsets of buyers
within a market that share similar needs and demonstrate similar buyer behaviour. The customers are
divided into segments based on their buying behaviour, and it might happen that a group includes
seemingly different customers from manufacturing, retail, and oil and gas, but their buying behavior would
be the same.
•Cross-sectional forecasting: On several occasions, we may use the information on the cases that we have
observed to predict the value of something we have not observed. This is mostly used in share market
analysis for determining the equity premium by using general statistical methods for testing stock-return
predictability based on endogenous variables. A similar concept can also be applied to forecast the sales
time series with the cross-sectional price of risk, which is strongly correlated with the market’s yield
measures.

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Time series analysis
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•Time series forecasting models try to predict the future based on past data. For example, sales figures
collected for the past six weeks can be used to forecast sales for the seventh week. Quarterly sales figures
collected for the past several years can be used to forecast future quarters. Even though both examples
contain sales, different forecasting time series models would likely be used.

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Time series analysis
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•Which forecasting model a firm should choose depends on
1.Time horizon to forecast.
2.Data availability.
3.Accuracy required.
4.Size of forecasting budget.
5.Availability of qualified personnel.
•In selecting a forecasting model, there are other issues such as the firm’s degree of flexibility. (The greater
the ability to react quickly to changes, the less accurate the forecast needs to be.)
•Another item is the consequence of a bad forecast. If a large capital investment decision is to be based on
a forecast, it should be a good forecast.

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Simple Moving Average
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•When demand for a product is neither growing nor declining rapidly, and if it does not have seasonal
characteristics, a moving average can be useful in removing the random fluctuations for forecasting.
•Although moving averages are frequently centered, it is more convenient to use past data to predict the
following period directly.
•To illustrate, a centered five-month average of January, February, March, April, and May gives an average
centered on March. However, all five months of data must already exist. If our objective is to forecast for
June, we must project our moving average—by some means—from March to June. If the average is not
centered but is at the forward end, we can forecast more easily, though we may lose some accuracy. Thus,
if we want to forecast June with a five-month moving average, we can take the average of January,
February, March, April, and May. When June passes, the forecast for July would be the average of
February, March, April, May, and June.

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Forecast Demand Based on a Three- and a Nine-Week
Simple Moving Average
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Moving Average Forecast of Three- and Nine-Week Periods
versus Actual Demand
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Simple Moving Average
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•Although it is important to select the best period for the moving average, there are several conflicting
effects of different period lengths.
•The longer the moving average period, the more the random elements are smoothed (which may be
desirable in many cases).
•But if there is a trend in the data—either increasing or decreasing—the moving average has the adverse
characteristic of lagging the trend.
•Therefore, while a shorter time span produces more oscillation, there is a closer following of the trend.
•Conversely, a longer time span gives a smoother response but lags the trend.

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Simple Moving Average
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•The above plot of the data, shows the effects of various lengths of the period of a moving average. We see
that the growth trend levels off at about the 23rd week. The three-week moving average responds better in
following this change than the nine-week average, although overall, the nine-week average is smoother.
The main disadvantage in calculating a moving average is that all individual elements must be carried as
data because a new forecast period involves adding new data and dropping the earliest data. For a three-
or six-period moving average, this is not too severe. But plotting a 60-day moving average for the usage of
each of 20,000 items in inventory would involve a significant amount of data.

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Weighted Moving Average
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•Whereas the simple moving average gives equal weight to each component of the moving average
database, a weighted moving average allows any weights to be placed on each element, providing, of
course, that the sum of all weights equals 1. For example, a department store may find that in a four-month
period, the best forecast is derived by using 40 percent of the actual sales for the most recent month, 30
percent of two months ago, 20 percent of three months ago, and 10 percent of four months ago. If actual
sales experience was
the forecast for month 5 would be

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•Although many periods may be ignored (that is, their weights are zero) and the weighting scheme may be
in any order (for example, more distant data may have greater weights than more recent data), the sum of
all the weights must equal 1.
Weighted Moving Average
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Choosing Weights
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•Experience and trial and error are the simplest ways to choose weights. As a general rule, the most recent
past is the most important indicator of what to expect in the future, and, therefore, it should get higher
weighting. The past month’s revenue or plant capacity, for example, would be a better estimate for the
coming month than the revenue or plant capacity of several months ago.
•However, if the data are seasonal, for example, weights should be established accordingly. Bathing suit
sales in July of last year should be weighted more heavily than bathing suit sales in December (in the
Northern Hemisphere).The weighted moving average has a definite advantage over the simple moving
average in being able to vary the effects of past data.

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Exponential Smoothing
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•In the previous methods of forecasting (simple and weighted moving averages), the major drawback is the
need to continually carry a large amount of historical data.
•As each new piece of data is added in these methods, the oldest observation is dropped, and the new
forecast is calculated.
•In many applications (perhaps in most), the most recent occurrences are more indicative of the future than
those in the more distant past.
•If this premise is valid—that the importance of data diminishes as the past becomes more distant—then
exponential smoothing may be the most logical and easiest method to use.
•The reason this is called exponential smoothing is that each increment in the past is decreased by (1 − α).
If α is 0.05, for example, weights for various periods would be as follows (α is defined below):

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Exponential Smoothing
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•Exponential smoothing is the most used of all forecasting techniques. It is an integral part of virtually all
computerized forecasting programs, and it is widely used in ordering inventory in retail firms, wholesale
companies, and service agencies.
•Exponential smoothing techniques have become well accepted for six major reasons:
1.Exponential models are surprisingly accurate.
2.Formulating an exponential model is relatively easy.
3.The user can understand how the model works.
4.Little computation is required to use the model.
5.Computer storage requirements are small because of the limited use of historical data.
6.Tests for accuracy as to how well the model is performing are easy to compute.

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Exponential Smoothing
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•In the exponential smoothing method, only three pieces of data are needed to forecast the future: the most
recent forecast, the actual demand that occurred for that forecast period, and a smoothing constant
alpha ().
•This smoothing constant determines the level of smoothing and the speed of reaction to differences
between forecasts and actual occurrences.
•The value for the constant is determined both by the nature of the product and by the manager’s sense of
what constitutes a good response rate.
•For example, if a firm produced a standard item with relatively stable demand, the reaction rate to
differences between actual and forecast demand would tend to be small, perhaps just 5 or 10 percentage
points. However, if the firm were experiencing growth, it would be desirable to have a higher reaction rate,
perhaps 15 to 30 percentage points, to give greater importance to recent growth experience. The more
rapid the growth, the higher the reaction rate should be. Sometimes users of the simple moving average
switch to exponential smoothing but like to keep the forecasts about the same as the simple moving
average. In this case, α is approximated by 2 ÷ (n + 1), where n is the number of time periods.

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Exponential Smoothing
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•This equation states that the new forecast is equal to the old forecast plus a portion of the error (the
difference between the previous forecast and what actually occurred). To demonstrate the method, assume
that the long-run demand for the product under study is relatively stable and a smoothing constant (α) of
0.05 is considered appropriate. If the exponential method were used as a continuing policy, a forecast
would have been made for last month. Assume that last month’s forecast (F
t−1) was 1,050 units. If 1,000
actually were demanded, rather than 1,050, the forecast for this month would be

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Exponential Forecasts versus Actual Demand for Units of a
Product over Time Showing the Forecast Lag
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Exponential Smoothing
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•Because the smoothing coefficient is small, the reaction of the new forecast to an error of 50 units is to
decrease the next month’s forecast by only 2 ½ units.
•Single exponential smoothing has the shortcoming of lagging changes in demand.
•The forecast lags during an increase or decrease but overshoots when a change in direction occurs.
•Note that the higher the value of alpha, the more closely the forecast follows the actual.
•To more closely track actual demand, a trend factor may be added.
•Adjusting the value of alpha also helps.
•This is termed adaptive forecasting.

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Trend Effects in Exponential Smoothing
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•Remember that an upward or downward trend in data collected over a sequence of time periods causes
the exponential forecast to always lag behind (be above or below) the actual occurrence.
•Exponentially smoothed forecasts can be corrected somewhat by adding in a trend adjustment.
•To correct the trend, we need two smoothing constants. Besides the smoothing constant α, the trend
equation also uses a smoothing constant delta ().
•The delta reduces the impact of the error that occurs between the actual and the forecast.
•If both alpha and delta are not included, the trend overreacts to errors.
•To get the trend equation going, the first time it is used the trend value must be entered manually.
•This initial trend value can be an educated guess, or a computation based on observed past data.

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Trend Effects in Exponential Smoothing
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Example: Forecast Including Trend
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•Assume an initial starting F
t of 100 units, a trend of 10 units, an alpha of .20, and a delta of .30. If actual
demand turned out to be 115 rather than the forecast 100, calculate the forecast for the next period.
•If, instead of 121.3, the actual turned out to be 120, the sequence would be repeated and the forecast for
the next period would be

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Choosing the Appropriate Value for Alpha
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•Exponential smoothing requires that the smoothing constant alpha (α) be given a value between 0 and 1. If
the real demand is stable (such as demand for electricity or food), we would like a small alpha to lessen
the effects of short-term or random changes.
•If the real demand is rapidly increasing or decreasing (such as in fashion items or new small appliances),
we would like a large alpha to try to keep up with the change.
•It would be ideal if we could predict which alpha we should use. Unfortunately, two things work against us.
First, it would take some passage of time to determine the alpha that would best fit our actual data. This
would be tedious to follow and revise. Second, because demands do change, the alpha we pick this week
may need to be revised soon. Therefore, we need some automatic method to track and change our alpha
values. There are two approaches to controlling the value of alpha. One uses various values of alpha. The
other uses a tracking signal.
1.Two or more predetermined values of alpha. The amount of error between the forecast and the actual demand is
measured. Depending on the degree of error, different values of alpha are used. If the error is large, alpha is 0.8; if the error
is small, alpha is 0.2.
2.Computed values for alpha. A tracking alpha computes whether the forecast is keeping pace with genuine upward or
downward changes in demand (as opposed to random changes). In this application, the tracking alpha is defined as the
exponentially smoothed actual error divided by the exponentially smoothed absolute error. Alpha changes from period to
period within the possible range of 0 to 1.

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Forecast Errors
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•In using the word error, we are referring to the difference between the forecast value and what actually
occurred.
•In statistics, these errors are called residuals.
•As long as the forecast value is within the confidence limits, this is not really an error.
•But common usage refers to the difference as an error.
•Demand for a product is generated through the interaction of a number of factors too complex to describe
accurately in a model.
•Therefore, all forecasts certainly contain some error.
•In discussing forecast errors, it is convenient to distinguish between sources of error and the measurement
of error.

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Sources of Error
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•Errors can come from a variety of sources. One common source that many forecasters are unaware of is
projecting past trends into the future.
•For example, when we talk about statistical errors in regression analysis, we are referring to the deviations
of observations from our regression line.
•It is common to attach a confidence band (that is, statistical control limits) to the regression line to reduce
the unexplained error.
•But when we then use this regression line as a forecasting device by projecting it into the future, the error
may not be correctly defined by the projected confidence band.
•This is because the confidence interval is based on past data; it may not hold for projected data points and
therefore cannot be used with the same confidence.
•In fact, experience has shown that the actual errors tend to be greater than those predicted from forecast
models.

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Sources of Error
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•Errors can be classified as bias or random.
•Bias errors occur when a consistent mistake is made. Sources of bias include the failure to include the
right variables; the use of the wrong relationships among variables; employing of the wrong trend line; a
mistaken shift in the seasonal demand from where it normally occurs; and the existence of some
undetected secular trend.
•Random errors can be defined as those that cannot be explained by the forecast model being used.

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Measurement of Error
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•Several common terms used to describe the degree of error are standard error, mean squared error (or
variance), and mean absolute deviation. In addition, tracking signals may be used to indicate any positive
or negative bias in the forecast.
•Standard error is discussed in the section on linear regression. Because the standard error is the square
root of a function, it is often more convenient to use the function itself. This is called the mean square error
or variance.
•The mean absolute deviation (MAD) was in vogue in the past but subsequently was ignored in favor of
standard deviation and standard error measures. In recent years, MAD has made a comeback because of
its simplicity and usefulness in obtaining tracking signals.
•MAD is the average error in the forecasts, using absolute values. It is valuable because MAD, like the
standard deviation, measures the dispersion of some observed value from some expected value.

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Measurement of Error
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•MAD is computed using the differences between the actual demand and the forecast demand without
regard to sign. It equals the sum of the absolute deviations divided by the number of data points, or, stated
in equation form,

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•When the errors that occur in the forecast are normally distributed (the usual case), the mean absolute
deviation relates to the standard deviation as
•The standard deviation is the larger measure. If the MAD of a set of points was found to be 60 units, then
the standard deviation would be 75 units. In the usual statistical manner, if control limits were set at plus or
minus 3 standard deviations (or ±3.75 MADs), then 99.7 percent of the points would fall within these limits.
•A tracking signal is a measurement that indicates whether the forecast average is keeping pace with any
genuine upward or downward changes in demand. As used in forecasting, the tracking signal is the
number of mean absolute deviations that the forecast value is above or below the actual occurrence. Thus,
if we compute the tracking signal and find it equal to minus 2, we can see that the forecast model is
providing forecasts that are quite a bit above the mean of the actual occurrences.
Measurement of Error
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A Normal Distribution with Mean = 0 and MAD = 1
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Measurement of Error
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•A tracking signal (TS) can be calculated using the arithmetic sum of forecast deviations divided by the
mean absolute deviation:

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Computing the Mean Absolute Deviation (MAD), the Running
Sum of Forecast Errors (RSFE), and the Tracking Signal (TS)
from Forecast and Actual Data
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Measurement of Error
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•Table in the previous slide illustrates the procedure for computing MAD and the tracking signal for a six-
month period where the forecast had been set at a constant 1,000 and the actual demands that occurred
are as shown.
•In this example, the forecast, on the average, was off by 66.7 units and the tracking signal was equal to 3.3
mean absolute deviations.
•We can get a better feel for what the MAD and tracking signal mean by plotting the points on a graph.
•Though this is not completely legitimate from a sample-size standpoint, we plotted each month in the next
slide to show the drift of the tracking signal.
•Note that it drifted from minus 1 MAD to plus 3.3 MADs.
•This happened because actual demand was greater than the forecast in four of the six periods.
•If the actual demand does not fall below the forecast to offset the continual positive RSFE, the tracking
signal would continue to rise, and we would conclude that assuming a demand of 1,000 is a bad forecast.

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A Plot of the Tracking Signals Calculated above
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Linear Regression Analysis
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•Regression can be defined as a functional relationship between two or more correlated variables. It is used
to predict one variable given the other. The relationship is usually developed from observed data. The data
should be plotted first to see if they appear linear or if at least parts of the data are linear. Linear regression
refers to the special class of regression where the relationship between variables forms a straight line.
•The linear regression line is of the form Y = a + bX, where Y is the value of the dependent variable that we
are solving for, a is the Y intercept, b is the slope, and X is the independent variable (actually there can be
many of these). In time series analysis, X is units of time.
•Linear regression is useful for long-term forecasting of major occurrences and aggregate planning. For
example, linear regression would be very useful to forecast demands for product families. Even though
demand for individual products within a family may vary widely during a time period, demand for the total
product family is surprisingly smooth.

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Linear regression forecasting
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•The major restriction in using linear regression forecasting is, as the name implies, that past data and
future projections are assumed to fall about a straight line.
•Although this does limit its application, sometimes, if we use a shorter period of time, linear regression
analysis can still be used.
•For example, there may be short segments of the longer period that are approximately linear.
•Linear regression is used both for time series forecasting and for causal relationship forecasting.
•When the dependent variable (usually the vertical axis on a graph) changes as a result of time (plotted as
the horizontal axis), it is time series analysis.
•If one variable changes because of the change in another variable, this is a causal relationship (such as
the number of deaths from lung cancer increasing with the number of people who smoke).

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Least Squares Method
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•Afirm’s sales for a product line during the 12 quarters of the past three years were as follows:
The firm wants to forecast each quarter of the fourth year—that is, quarters 13, 14, 15, and 16.

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SOLUTION
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•The least squares equation for linear regression is
•The least squares method tries to fit the line to the data that minimizes the sum of the squares of the
vertical distance between each data point and its corresponding point on the line. If a straight line is drawn
through the general area of the points, the difference between the point and the line is y − Y.

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Least Squares Regression Line
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SOLUTION
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•The sum of the squares of the differences between the plotted data points and the line points is
•The best line to use is the one that minimizes this total.
•As before, the straight-line equation is
•Previously we determined a and b from the graph. In the least squares method, the equations for a and b
are

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Least Squares Regression Analysis
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SOLUTION
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•These computations carried out for the 12 data points in the problem. Note that the final equation for Y
shows an intercept of 441.6 and a slope of 359.6. The slope shows that for every unit change in X, Y
changes by 359.6.
•Strictly based on the equation, forecasts for periods 13 through 16 would be
•The standard error of estimate, or how well the line fits the data, is

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SOLUTION
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•The standard error of estimate is computed from the second and last columns

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Excel Regression Tool
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