Discussion – Operation Management

Textbook: Stevenson, W. (2021). Operations management (14th ed.). New York, NY:
McGraw-Hill Irwin
Important: Use Textbook + 1-2 scholarly reference in APA style.
Operations Management
Read through the Case Study entitled “Highline Financial Services, Ltd.” in Chapter 3
of your textbook. Examine the historical trends this company has experienced for the
three products (A, B, C) discussed over the two years shown.
Address the following requirements:
•

Prepare demand forecasts for the next four quarters for all three products,
describe the forecasting method you chose and explain why that forecasting
method is best suited to the scenario.

•

Explain why you did, or did not, choose the same forecasting method for each
product.

•

What are the benefits of using a formalized approach to forecasting these
products?

Student types answers here.
Directions:
•

Discuss the concepts, principles, and theories from your textbook. Cite your
textbook.

•

Provide opinions, examples, of hypotheticals.

•

Your initial post should address all components of the question with a 500 word
limit.

•

Important: Use Textbook + 1-2 scholarly reference in APA style.

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3

Forecasting

C H A P T E R

LEARNING OBJECTIVES
After completing this chapter, you should be able to:
LO#.$

List features common to all forecasts.

LO#.%

Explain why forecasts are generally wrong.

LO#.#

List the elements of a good forecast.

LO#.”

Outline the steps in the forecasting process.

LO#.&

Describe four qualitative forecasting techniques.

LO#.’

Use a naive method to make a forecast.

LO#.!

Prepare a moving average forecast.

LO#.(

Prepare a weighted-average forecast.

LO#.)

Prepare an exponential smoothing forecast.

LO#.$*

Prepare a linear trend forecast.

LO#.$$

Prepare a trend-adjusted exponential smoothing forecast.

LO#.$%

Compute and use seasonal relatives.

LO#.$#

Compute and use regression and correlation coefficients.

LO#.$”

Summarize forecast errors and use summaries to make!decisions.

LO#.$&

Construct control charts and use them to monitor forecast!errors.

LO#.$’

Describe the key factors and trade-offs to consider when choosing a forecasting technique.

C H A P T E R
#.$
#.%
#.#
#.”
#.&

O U T L I N E

Introduction !”
Features Common to All
Forecasts !#
Elements of a Good
Forecast !#
Forecasting and the Supply
Chain !$
Steps in the Forecasting
Process !$

#.’

Approaches to
Forecasting #%

#.!

Qualitative Forecasts #%
Executive Opinions #%
Salesforce Opinions #&
Consumer Surveys #&
Other Approaches #&

#.(

Forecasts Based on TimeSeries Data #’
Naive Methods #’
Techniques For Averaging #(
Other Forecasting Methods ##
Techniques For Trend #$
Trend-Adjusted Exponential
Smoothing $’

!”

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Photodisc/Getty Images

Techniques For
Seasonality $)
Techniques For Cycles $#

#.)

Associative Forecasting
Techniques $#
Simple Linear Regression $#
Comments On The Use Of
Linear Regression Analysis &%’

Nonlinear And Multiple
Regression Analysis &%(

#.$* Forecast Accuracy &%(
Summarizing Forecast
Accuracy &%”

#.$$ Monitoring Forecast Error &%!
#.$% Choosing a Forecasting
Technique &&&

#.$# Using Forecast Information &&’
#.$” Computer Software in
Forecasting &&)
#.$& Operations Strategy &&)
Cases: M&L Manufacturing &)”
Highline Financial Services,
Ltd., &)!

Weather forecasts are one of the many types of forecasts used by some business organizations. Although some businesses simply rely on publicly available weather forecasts, others turn to firms that specialize in weather-related forecasts. For example, Home Depot, Gap, and JCPenney use such firms to help them take weather factors into account for
estimating demand.
Many new car buyers have a thing or two in common. Once they make the decision to buy a new car, they want it
as soon as possible. They usually don’t want to order it and then have to wait six weeks or more for delivery. If the car
dealer they visit doesn’t have the car they want, they’ll look elsewhere. Hence, it is important for a dealer to anticipate
buyer wants and to have those models, with the necessary options, in stock. The dealer who can correctly forecast
buyer wants, and have those cars available, is going to be much more successful than a competitor who guesses
instead of forecasting—and guesses wrong—and gets stuck with cars customers don’t want. So how does the dealer
know how many cars of each type to stock? The answer is, the dealer doesn’t know for sure, but by analyzing previous buying patterns, and perhaps making allowances for current conditions, the dealer can come up with a reasonable
approximation of what buyers will want.
Planning is an integral part of a manager’s job. If uncertainties cloud the planning horizon, managers will find it difficult to plan effectively. Forecasts help managers by reducing some of the uncertainty, thereby enabling them to develop
continued
!&

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Chapter Three Forecasting

!”

more meaningful plans. A forecast is an estimate about the future value of a variable
such as demand. The better the estimate, the more informed decisions can be. Some
forecasts are long range, covering several years or more. Long-range forecasts are
especially important for decisions that will have long-term consequences for an organization or for a town, city, country,
state, or nation. One example is deciding on the right capacity for a planned power plant that will operate for the next
!” years. Other forecasts are used to determine if there is a profit potential for a new service or a new product: Will
there be sufficient demand to make the innovation worthwhile? Many forecasts are short term, covering a day or week.
They are especially helpful in planning and scheduling day-to-day operations. This chapter provides a survey of business
forecasting. It describes the elements of good forecasts, the necessary steps in preparing a forecast, basic forecasting
techniques, and how to monitor a forecast.
Forecast A statement about
the future value of a variable
of interest.

#.$ INTRODUCTION
Forecasts are a basic input in the decision processes of operations management because they
provide information on future demand. The importance of forecasting to operations management cannot be overstated. The primary goal of operations management is to match supply
to demand. Having a forecast of demand is essential for determining how much capacity or
supply will be needed to meet demand. For instance, operations needs to know what capacity
will be needed to make staffing and equipment decisions, budgets must be prepared, purchasing needs information for ordering from suppliers, and supply chain partners need to make
their plans.
Businesses make plans for future operations based on anticipated future demand. Anticipated demand is derived from two possible sources, actual customer orders and forecasts. For
businesses where customer orders make up most or all of anticipated demand, planning is
straightforward, and little or no forecasting is needed. However, for many businesses, most or
all of anticipated demand is derived from forecasts.
Two aspects of forecasts are important. One is the expected level of demand; the other is
the degree of accuracy that can be assigned to a forecast (i.e., the potential size of forecast
error). The expected level of demand can be a function of some structural variation, such as a
trend or seasonal variation. Forecast accuracy is a function of the ability of forecasters to correctly model demand, random variation, and sometimes unforeseen events.
Forecasts are made with reference to a specific time horizon. The time horizon may be fairly
short (e.g., an hour, day, week, or month), or somewhat longer (e.g., the next six months, the
next year, the next five years, or the life of a product or service). Short-term forecasts pertain
to ongoing operations. Long-range forecasts can be an important strategic planning tool. Longterm forecasts pertain to new products or services, new equipment, new facilities, or something
else that will require a somewhat long lead time to develop, construct, or otherwise implement.
Forecasts are the basis for budgeting, planning capacity, sales, production and inventory,
personnel, purchasing, and more. Forecasts play an important role in the planning process
because they enable managers to anticipate the future so they can plan accordingly.
Forecasts affect decisions and activities throughout an organization, in accounting,
finance, human resources, marketing, and management information systems (MIS), as well as
in operations and other parts of an organization. Here are some examples of uses of forecasts
in business organizations:
Accounting. New product/process cost estimates, profit projections, cash management.
Finance. Equipment/equipment replacement needs, timing and amount of funding/borrowing needs.
Human resources. Hiring activities, including recruitment, interviewing, and training;
layoff planning, including outplacement counseling.

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Chapter Three Forecasting

!!

Marketing. Pricing and promotion, e-business strategies, global competition strategies.
MIS. New/revised information systems, internet services.
Operations. Schedules, capacity planning, work assignments and workloads, inventory
planning, make-or-buy decisions, outsourcing, project management.
Product/service design. Revision of current features, design of new products or services.
In most of these uses of forecasts, decisions in one area have consequences in other areas.
Therefore, it is very important for all affected areas to agree on a common forecast. However, this may not be easy to accomplish. Different departments often have very different
perspectives on a forecast, making a consensus forecast difficult to achieve. For example,
salespeople, by their very nature, may be overly optimistic with their forecasts, and may want
to “reserve” capacity for their customers. This can result in excess costs for operations and
inventory storage. Conversely, if demand exceeds forecasts, operations and the supply chain
may not be able to meet demand, which would mean lost business and dissatisfied customers.
Forecasting is also an important component of yield management, which relates to!the percentage of capacity being used. Accurate forecasts can help managers plan tactics (e.g.,!offer
discounts, don’t offer discounts) to match capacity with demand, thereby achieving highyield levels.
There are two uses for forecasts. One is to help managers plan the system, and the other
is to help them plan the use of the system. Planning the system generally involves long-range
plans about the types of products and services to offer, what facilities and equipment to
have, where to locate, and so on. Planning the use of the system refers to short-range and
intermediate-range planning, which involve tasks such as planning inventory and workforce
levels, planning purchasing and production, budgeting, and scheduling.
Business forecasting pertains to more than predicting demand. Forecasts are also used to
predict profits, revenues, costs, productivity changes, prices and availability of energy and
raw materials, interest rates, movements of key economic indicators (e.g., gross domestic
product, inflation, government borrowing), and prices of stocks and bonds. For the sake of
simplicity, this chapter will focus on the forecasting of demand. Keep in mind, however, that
the concepts and techniques apply equally well to the other variables.
The Walt Disney World forecasting
department has !” employees who
formulate forecasts on volume and
revenue for the theme parks, water
parks, resort hotels, as well as
merchandise, food, and beverage
revenue by location.

Peter Cosgrove/AP Images

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!#

Chapter Three Forecasting

Despite of its use of computers and sophisticated mathematical models, forecasting is not
an exact science. Instead, successful forecasting often requires a skillful blending of science
and intuition. Experience, judgment, and technical expertise all play a role in developing useful forecasts. Along with these, a certain amount of luck and a dash of humility can be helpful,
because the worst forecasters occasionally produce a very good forecast, and even the best forecasters sometimes miss completely. Current forecasting techniques range from the mundane to
the exotic. Some work better than others, but no single technique works all the time.

LO#.$ List features common to all forecasts.

LO#.% Explain why forecasts are generally wrong.

#.% FEATURES COMMON TO ALL FORECASTS
A wide variety of forecasting techniques are in use. In many respects, they are quite different
from each other, as you shall soon discover. Nonetheless, certain features are common to all,
and it is important to recognize them.
• Forecasting techniques generally assume that the same underlying causal system that
existed in the past will continue to exist in the future.

Comment A manager cannot simply delegate forecasting to models or computers and then
forget about it, because unplanned occurrences can wreak havoc with forecasts. For instance,
weather-related events, tax increases or decreases, and changes in features or prices of competing
products or services can have a major impact on demand. Consequently, a manager must be alert
to such occurrences and be ready to override forecasts, which assume a stable causal system.
• Forecasts are not perfect; actual results usually differ from predicted values; the presence of randomness precludes a perfect forecast. Allowances should be made for forecast errors.
• Forecasts for groups of items tend to be more accurate than forecasts for individual
items because forecasting errors among items in a group usually have a canceling effect.
Opportunities for grouping may arise if parts or raw materials are used for multiple
products or if a product or service is demanded by a number of independent sources.
• Forecast accuracy decreases as the time period covered by the forecast—the time
horizon—increases. Generally speaking, short-range forecasts must contend with fewer
uncertainties than longer-range forecasts, so they tend to be more accurate.
An important consequence of the last point is that flexible business organizations—those
that can respond quickly to changes in demand—require a shorter forecasting horizon and,
hence, benefit from more accurate short-range forecasts than competitors who are less flexible and who must therefore use longer forecast horizons.

LO#.# List the elements
of a good forecast.

#.# ELEMENTS OF A GOOD FORECAST
A properly prepared forecast should fulfill certain requirements:
• The forecast should be timely. Usually, a certain amount of time is needed to respond to
the information contained in a forecast. For example, capacity cannot be expanded overnight, nor can inventory levels be changed immediately. Hence, the forecasting horizon
must cover the time necessary to implement possible changes.
• The forecast should be accurate, and the degree of accuracy should be stated. This will
enable users to plan for possible errors and will provide a basis for comparing alternative forecasts.
• The forecast should be reliable; it should work consistently. A technique that sometimes
provides a good forecast and sometimes a poor one will leave users with the uneasy
feeling that they may get burned every time a new forecast is issued.

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Chapter Three Forecasting

!$

• The forecast should be expressed in meaningful units. Financial planners need to know
how many dollars will be needed, production planners need to know how many units
will be needed, and schedulers need to know what machines and skills will be required.
The choice of units depends on user needs.
• The forecast should be in writing. Although this will not guarantee that all concerned are
using the same information, it will at least increase the likelihood of it. In addition, a written
forecast will permit an objective basis for evaluating the forecast once actual results are in.
• The forecasting technique should be simple to understand and use. Users often lack
confidence in forecasts based on sophisticated techniques; they do not understand either
the circumstances in which the techniques are appropriate or the limitations of the techniques. Misuse of techniques is an obvious consequence. Not surprisingly, fairly simple
forecasting techniques enjoy widespread popularity because users are more comfortable
working with them.
• The forecast should be cost-effective: The benefits should outweigh the costs.

#.” FORECASTING AND THE SUPPLY CHAIN
Accurate forecasts are very important for the supply chain. Inaccurate forecasts can lead to
shortages and excesses throughout the supply chain. Shortages of materials, parts, and services
can lead to missed deliveries, work disruption, and poor customer service. Conversely, overly
optimistic forecasts can lead to excesses of materials and/or capacity, which increase costs.
Both shortages and excesses in the supply chain have a negative impact not only on customer
service but also on profits. Furthermore, inaccurate forecasts can result in temporary increases
and decreases in orders to the supply chain, which can be misinterpreted by the supply chain.
Organizations can reduce the likelihood of such occurrences in a number of ways. One,
obviously, is by striving to develop the best possible forecasts. Another is through collaborative planning and forecasting with major supply chain partners. Yet another way is through
information sharing among partners and perhaps increasing supply chain visibility by allowing supply chain partners to have real-time access to sales and inventory information. Also
important is rapid communication about poor forecasts, as well as about unplanned events
that disrupt operations (e.g., flooding, work stoppages), and changes in plans.

#.& STEPS IN THE FORECASTING PROCESS
There are six basic steps in the forecasting process:
1.

2.
3.

4.
5.
6.

LO#.” Outline the steps
in the forecasting process.

Determine the purpose of the forecast. How will it be used and when will it be
needed? This step will provide an indication of the level of detail required in the forecast, the amount of resources (personnel, computer time, dollars) that can be justified,
and the level of accuracy necessary.
Establish a time horizon. The forecast must indicate a time interval, keeping in mind
that accuracy decreases as the time horizon increases.
Obtain, clean, and analyze appropriate data. Obtaining the data can involve significant effort. Once obtained, the data may need to be “cleaned” to get rid of outliers and
obviously incorrect data before analysis.
Select a forecasting technique.
Make the forecast.
Monitor the forecast errors. The forecast errors should be monitored to determine if!the
forecast is performing in a satisfactory manner. If it is not, reexamine the method, assumptions, the validity of data, and so on; modify as needed; and prepare a revised!forecast.

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#%

Chapter Three Forecasting

Once the process has been set up, it may only be necessary to repeat steps 3 and 6 as new
data become available.
Note, too, that additional action may be necessary. For example, if demand was much less
than the forecast, an action such as a price reduction or a promotion may be needed. Conversely, if demand was much more than predicted, increased output may be advantageous.
That may involve working overtime, outsourcing, or taking other measures.

#.’ APPROACHES TO FORECASTING

Judgmental forecasts Forecasts that use subjective
inputs such as opinions from
consumer surveys, sales staff,
managers, executives, and
experts.
Time-series forecasts Forecasts that project patterns
identified in recent time-series
observations.
Associative model Forecasting technique that uses
explanatory variables to predict future demand.
LO#.& Describe four
qualitative forecasting
techniques.

There are two general approaches to forecasting: qualitative and quantitative. Qualitative
methods consist mainly of subjective inputs, which often defy precise numerical description.
Quantitative methods involve either the projection of historical data or the development of
associative models that attempt to utilize causal (explanatory) variables to make a forecast.
Qualitative techniques permit inclusion of soft information (e.g., human factors, personal
opinions, hunches) in the forecasting process. Those factors are often omitted or downplayed
when quantitative techniques are used because they are difficult or impossible to quantify.
Quantitative techniques consist mainly of analyzing objective, or hard, data. They usually
avoid personal biases that sometimes contaminate qualitative methods. In practice, either
approach, or a combination of both approaches, might be used to develop a forecast.
The following pages present a variety of forecasting techniques that are classified as judgmental, time-series, or associative.
Judgmental forecasts rely on analysis of subjective inputs obtained from various sources,
such as consumer surveys, the sales staff, managers and executives, and panels of experts.
Quite frequently, these sources provide insights that are not otherwise available.
Time-series forecasts simply attempt to project past experience into the future. These
techniques use historical data with the assumption that the future will be like the past. Some
models merely attempt to smooth out random variations in historical data; others attempt to
identify specific patterns in the data and project or extrapolate those patterns into the future,
without trying to identify causes of the patterns.
Associative models use equations that consist of one or more explanatory variables that
can be used to predict demand. For example, demand for paint might be related to variables
such as the price per gallon and the amount spent on advertising, as well as to specific characteristics of the paint (e.g., drying time, ease of cleanup).

#.! QUALITATIVE FORECASTS
In some situations, forecasters rely solely on judgment and opinion to make forecasts. If
management must have a forecast quickly, there may not be enough time to gather and analyze quantitative data. At other times, especially when political and economic conditions are
changing, available data may be obsolete, and more up-to-date information might not yet be
available. Similarly, the introduction of new products and the redesign of existing products or
packaging suffer from the absence of historical data that would be useful in forecasting. In
such instances, forecasts are based on executive opinions, consumer surveys, opinions of the
sales staff, and opinions of experts.

Executive Opinions
A small group of upper-level managers (e.g., in marketing, operations, and finance) may meet
and collectively develop a forecast. This approach is often used as a part of long-range planning and new product development. It has the advantage of bringing together the considerable knowledge and talents of various managers. However, there is the risk that the view of
one!person will prevail, and the possibility that diffusing responsibility for the forecast over
the entire group may result in less pressure to produce a good forecast.

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Chapter Three Forecasting

#&

Salesforce Opinions
Members of the sales staff or the customer service staff are often good sources of information because of their direct contact with consumers. They are often aware of any plans the
customers may be considering for the future. There are, however, several drawbacks to using
salesforce opinions. One is that staff members may be unable to distinguish between what
customers would like to do and what they actually will do. Another is that these people are
sometimes overly influenced by recent experiences. Thus, after several periods of low sales,
their estimates may tend to become pessimistic. After several periods of good sales, they
may tend to be too optimistic. In addition, if forecasts are used to establish sales quotas,
there will be a conflict of interest because it is to the salesperson’s advantage to provide low
sales!estimates.

Consumer Surveys
Because it is the consumers who ultimately determine demand, it seems natural to solicit
input from them. In some instances, every customer or potential customer can be contacted.
However, usually there are too many customers or there is no way to identify all potential customers. Therefore, organizations seeking consumer input usually resort to consumer
surveys, which enable them to sample consumer opinions. The obvious advantage of consumer surveys is that they can tap information that might not be available elsewhere. On
the other hand, a considerable amount of knowledge and skill is required to construct a
survey, administer it, and correctly interpret the results for valid information. Surveys can
be expensive and time-consuming. In addition, even under the best conditions, surveys of
the general public must contend with the possibility of irrational behavior patterns. For
example, much of the consumer’s thoughtful information gathering before purchasing a
new car is often undermined by the glitter of a new car showroom or a high-pressure sales
pitch. Along the same lines, low response rates to a mail survey should—but often don’t—
make the results suspect.
If these and similar pitfalls can be avoided, surveys can produce useful information.

Other Approaches
A manager may solicit opinions from a number of other managers and staff people. Occasionally, outside experts are needed to help with a forecast. Advice may be needed on political or
economic conditions in the United States or a foreign country, or some other aspect of importance with which an organization lacks familiarity.
Another approach is the Delphi method, an iterative process intended to achieve a consensus forecast. This method involves circulating a series of questionnaires among individuals who possess the knowledge and ability to contribute meaningfully. Responses are kept
anonymous, which tends to encourage honest responses and reduces the risk that one person’s
opinion will prevail. Each new questionnaire is developed using the information extracted
from the previous one, thus enlarging the scope of information on which participants can base
their judgments.
The Delphi method has been applied to a variety of situations, not all of which involve
forecasting. The discussion here is limited to its use as a forecasting tool.
As a forecasting tool, the Delphi method is useful for technological forecasting; that is,
for assessing changes in technology and their impact on an organization. Often, the goal is to
predict when a certain event will occur. For instance, the goal of a Delphi forecast might be to
predict when video telephones might be installed in at least 50 percent of residential homes or
when a vaccine for a disease might be developed and ready for mass distribution. For the most
part, these are long-term, single-time forecasts, which usually have very little hard information to go by or data that are costly to obtain, so the problem does not lend itself to analytical
techniques. Rather, judgments of experts or others who possess sufficient knowledge to make
predictions are used.

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Delphi method An iterative
process in which managers
and staff complete a series
of questionnaires, each
developed from the previous
one, to achieve a consensus
forecast.

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#’

Chapter Three Forecasting

#.( FORECASTS BASED ON TIME+SERIES DATA
Time series A time-ordered
sequence of observations
taken at regular intervals.

A time series is a time-ordered sequence of observations taken at regular intervals (e.g.,
hourly, daily, weekly, monthly, quarterly, annually). The data may be measurements of
demand, sales, earnings, profits, shipments, accidents, output, precipitation, productivity,
or the consumer price index. Note that forecasts based on sales will understate demand
when demand exceeds sales, causing shortages (stockouts) to occur. Forecasting techniques based on time-series data are made on the assumption that future values of the
series can be estimated from past values. Although no attempt is made to identify variables that influence the series, these methods are widely used, often with quite satisfactory results.
Analysis of time-series data requires the analyst to identify the underlying behavior of the
series. This can often be accomplished by merely plotting the data and visually examining
the plot. One or more patterns might appear: trends, seasonal variations, cycles, or variations
around an average. In addition, there will be random and perhaps irregular variations. These
behaviors can be described as follows:

Trend A long-term upward or
downward movement in data.

1.

Trend refers to a long-term upward or downward movement in the data. Population!shifts, changing incomes, and cultural changes often account for such
movements.

Seasonality Short-term regular variations related to the
calendar or time of day.

2.

Seasonality refers to short-term, fairly regular variations generally related to factors
such as the calendar or time of day. Restaurants, supermarkets, and theaters experience
weekly and even daily “seasonal” variations.

Cycle Wavelike variations
lasting more than one year.

3.

Cycles are wavelike variations of more than one year’s duration. These are often related
to a variety of economic, political, and even agricultural conditions.

Irregular variation Caused
by unusual circumstances, not
reflective of typical behavior.

4.

Irregular variations are due to unusual circumstances such as severe weather conditions, strikes, or a major change in a product or service. They do not reflect typical
behavior, and their inclusion in the series can distort the overall picture. Whenever possible, these should be identified and removed from the data.

Random variations Residual
variations after all other
behaviors are accounted for.

5.

Random variations are residual variations that remain after all other behaviors have
been accounted for.

These behaviors are illustrated in Figure 3.1. The small “bumps” in the plots represent
random variability.
The remainder of this section describes the various approaches to the analysis of timeseries data. Before turning to those discussions, one point should be emphasized: A demand
forecast should be based on a time series of past demand rather than unit sales. Sales would
not truly reflect demand if one or more stockouts occurred.

Naive Methods
Naive forecast A forecast
for any period that equals the
previous period’s actual value.
LO#.’ Use a naive
method to make a forecast.

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A simple but widely used approach to forecasting is the naive approach. A naive forecast
uses a single previous value of a time series as the basis of a forecast. The naive approach
can be used with a stable series (variations around an average), with seasonal variations,
or with trend. With a stable series, the last data point becomes the forecast for the next
period. Thus, if demand for a product last week was 20 cases, the forecast for this week is
20!cases. With seasonal variations, the forecast for this “season” is equal to the value of
the series last “season.” For example, the forecast for demand for turkeys this Thanksgiving season is equal to demand for turkeys last Thanksgiving; the forecast of the number of
checks cashed at a bank on the first day of the month next month is equal to the number
of!checks cashed on the first day of this month; and the forecast for highway traffic volume
this Friday is equal to the highway traffic volume last Friday. For data with trend, the forecast is equal to the last value of the series plus or minus the difference between the last two

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Chapter Three Forecasting
y

#(

FIGURE #.$

Irregular
variation

Trend, cyclical, and
seasonal data plots, with
random and irregular
variations

Trend

0

Time

y

Cycles

0

Time

y
Seasonal variations

Year 4

y

Year 3
y

Year 2

y
Year 1
F

J

M

A

M

J

J

A

S

O

N

D
Month

values of the series. For example, suppose the last two values were 50 and 53. The next
forecast would be 56:
Period

Actual

#

$”

%

$&

&

Change from
Previous Value

Forecast

+&
$& + & = $’

Although at first glance the naive approach may appear too simplistic, it is nonetheless a
legitimate forecasting tool. Consider the advantages: It has virtually no cost, it is quick and
easy to prepare because data analysis is nonexistent, and it is easily understandable. The
main objection to this method is its inability to provide highly accurate forecasts.!However, if resulting accuracy is acceptable, this approach deserves serious consideration.
Moreover, even if other forecasting techniques offer better accuracy, they will almost
always involve a greater cost. The accuracy of a naive forecast can serve as a standard of
comparison against which to judge the cost and accuracy of other techniques. Thus, managers must answer the question: Is the increased accuracy of another method worth the
additional resources required to achieve that accuracy?

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Chapter Three Forecasting

#)

FIGURE #.% Averaging applied to three possible patterns

Data
Forecast

Ideal

Step change

Gradual change

(Forecast lags)

(Forecast lags)

Techniques for Averaging
Historical data typically contain a certain amount of random variation, or white noise, that
tends to obscure systematic movements in the data. This randomness arises from the combined influence of many—perhaps a great many—relatively unimportant factors, and it cannot be reliably predicted. Averaging techniques smooth variations in the data. Ideally, it would
be desirable to completely remove any randomness from the data and leave only “real” variations, such as changes in the demand. As a practical matter, however, it is usually impossible
to distinguish between these two kinds of variations, so the best one can hope for is that the
small variations are random and the large variations are “real.”
Averaging techniques smooth fluctuations in a time series because the individual highs and
lows in the data offset each other when they are combined into an average. A forecast based
on an average thus tends to exhibit less variability than the original data (see Figure 3.2). This
can be advantageous because many of these movements merely reflect random variability
rather than a true change in the series. Moreover, because responding to changes in expected
demand often entails considerable cost (e.g., changes in production rate, changes in the size
of a workforce, inventory changes), it is desirable to avoid reacting to minor variations. Thus,
minor variations are treated as random variations, whereas larger variations are viewed as
more likely to reflect “real” changes, although these, too, are smoothed to a certain degree.
Averaging techniques generate forecasts that reflect recent values of a time series (e.g., the
average value over the last several periods). These techniques work best when a series tends to
vary around an average, although they also can handle step changes or gradual changes in the
level of the series. Three techniques for averaging are described in this section:
1.
2.
3.

Moving average Technique
that averages a number of
recent actual values, updated
as new values become
available.
LO#.! Prepare a moving
average forecast.

Moving average
Weighted moving average
Exponential smoothing

Moving Average One weakness of the naive method is that the forecast just traces the
actual data, with a lag of one period; it does not smooth at all. But by expanding the amount of
historical data a forecast is based on, this difficulty can be overcome. A moving average forecast uses a number of the most recent actual data values in generating a forecast. The moving
average forecast can be computed using the following equation:
n

∑ A t”i

At”n + # + At”2 + At”1
i=1
F t = MA n = ______
= ____________________
n
n

(3–1)

where
Ft = Forecast for time period t
MAn = n period moving average
At”i = Actual value in period t ” i
n = Number of periods (data points) in the moving average
For example, MA3 would refer to a three-period moving average forecast, and MA5 would
refer to a five-period moving average forecast.

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Chapter Three Forecasting

EXAMPLE

Computing a Moving Average
Compute a three-period moving average forecast given demand for shopping carts for the
last five periods.
Period

Demand

#

!%

%
&
!
$

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!&�
!”� the & most(recent(demands
!#�

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43 + 40 + 41
F6 = __________ = 41.33
3
If actual demand in period 6 turns out to be 38, the moving average forecast for period!7
would be
40 + 41 + 38
F7 = __________ = 39.67
3

S O L U T I O N

Note that in a moving average, as each new actual value becomes available, the forecast is
updated by adding the newest value and dropping the oldest and then recomputing the average. Consequently, the forecast “moves” by reflecting only the most recent values.
In computing a moving average, including a moving total column—which gives the sum of
the n most current values from which the average will be computed—aids computations. To
update the moving total: Subtract the oldest value from the newest value and add that amount
to the moving total for each update.
Figure 3.3 illustrates a three-period moving average forecast plotted against actual demand
over 31 periods. Note how the moving average forecast lags the actual values and how smooth
the forecasted values are compared with the actual values.
The moving average can incorporate as many data points as desired. In selecting the number
of periods to include, the decision maker must take into account that the number of data points
in the average determines its sensitivity to each new data point: The fewer the data points in an
average, the more sensitive (responsive) the average tends to be. (See Figure!3.4A.)
If responsiveness is important, a moving average with relatively few data points should
be used. This will permit quick adjustment to, say, a step change in the data, but it also will

FIGURE #.#

y

A moving average forecast
tends to smooth and lag
changes in the data

3-period moving average (MA)
Demand

50

Demand

40

30

20

10

0

5

10

15

20

25

30

t

Period

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Chapter Three Forecasting

#”

FIGURE #.”A

The more periods in a
moving average, the
greater the forecast will lag
changes in the data

40

Data
MA 3

Demand

35

MA 5

30

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Period

cause the forecast to be somewhat responsive even to random variations. Conversely, moving
averages based on more data points will smooth more but be less responsive to “real” changes.
Hence, the decision maker must weigh the cost of responding more slowly to changes in the
data against the cost of responding to what might simply be random variations. A review of
forecast errors can help in this decision.
The advantages of a moving average forecast are that it is easy to compute and easy to understand. A possible disadvantage is that all values in the average are weighted equally. For instance,
in a 10-period moving average, each value has a weight of 1/10. Hence, the oldest value has the
same weight as the most recent value. If a change occurs in the series, a moving average forecast
can be slow to react, especially if there are a large number of values in the!average. Decreasing
the number of values in the average increases the weight of more recent values, but it does so at
the expense of losing potential information from less recent values.
Weighted average More
recent values in a series are
given more weight in computing a forecast.
LO#.( Prepare a weightedaverage forecast.

Weighted Moving Average A weighted average is similar to a moving average, except
that it typically assigns more weight to the most recent values in a time series. For instance,
the most recent value might be assigned a weight of .40, the next most recent value a weight
of .30, the next after that a weight of .20, and the next after that a weight of .10. Note that the
weights must sum to 1.00, and that the heaviest weights are assigned to the most recent values.
Ft = wt”n( At”n) + # + wt”2( At”2) + wt”1( At”1) + # + wt”n( At”n)

(3–2)

where
wt”1 = Weight for period t ” 1, etc.
At”1 = Actual value for period t ” 1, etc.

EXAMPLE

%

Computing a Weighted Moving Average
Given the following demand data,

mhhe.com/stevenson14e

a.

Compute a weighted average forecast using a weight of .40 for the most recent period,
.30 for the next most recent, .20 for the next, and .10 for the next.

b.

If the actual demand for period 6 is 39, forecast demand for period 7 using the same
weights as in part a.
Period
#
%
&
!
$

ste3889X_ch03_074-137.indd 86

Demand
!%
!”
!&
!”
!#

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Chapter Three Forecasting

a.
b.

#!

S O L U T I O N

F6 = .10(40) + .20(43) + .30(40) + .40(41) = 41.0
F7 = .10(43) + .20(40) + .30(41) + .40(39) = 40.2

Note that if four weights are used, only the four most recent demands are used to prepare
the forecast.
The advantage of a weighted average over a simple moving average is that the weighted average is more reflective of the most recent occurrences. However, the choice of weights is somewhat
arbitrary and generally involves the use of trial and error to find a suitable weighting scheme.

Exponential Smoothing Exponential smoothing is a sophisticated weighted averaging
method that is still relatively easy to use and understand. 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. That is:

Exponential smoothing A
weighted averaging method
based on the previous forecast plus a percentage of the
forecast error.

Next forecast = Previous forecast + !(Actual ” Previous forecast)
where (Actual ” Previous forecast) represents the forecast error and ! is a percentage of the
error. More concisely,
Ft = Ft”1 + !( At”1 ” Ft”1)

(3–3a)

LO3.9 Prepare an
exponential smoothing
forecast.

where
Ft = Forecast for period t
Ft”1 = Forecast for the previous period (i.e., period t ” 1)
! = Smoothing constant (percentage, usually less than 50%)
At”1 = Actual demand or sales for the previous period
The smoothing constant ! represents a percentage of the forecast error. Each new forecast
is equal to the previous forecast plus a percentage of the previous error. For example, suppose
the previous forecast was 42 units, actual demand was 40 units, and ! = .10. The new forecast
would be computed as follows:
Ft = 42 + .10(40 ” 42 ) = 41.8
Then, if the actual demand turns out to be 43, the next forecast would be
Ft = 41.8 + .10(43 ” 41.8 ) = 41.92
An alternate form of Formula 3–3a reveals the weighting of the previous forecast and the
latest actual demand:
Ft = (1 ” !) Ft”1 + ! At”1

(3–3b)

For example, if ! = .10, this would be
Ft = .90 Ft”1 + .10 At”1
The quickness of forecast adjustment to error is determined by the smoothing constant,!!.
The closer its value is to zero, the slower the forecast will be to adjust to forecast errors
(i.e.,!the greater the smoothing). Conversely, the closer the value of ! is to 1.00, the greater
the responsiveness and the less the smoothing. This is illustrated in Figure 3.4B.

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##

FIGURE #.”B

The closer ! is to zero, the
greater the smoothing

Chapter Three Forecasting
Actual
Demand

Period (t)
#
%
&
!
$
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*
#”
##
#%

starting fo

!%
!”
!&
!”
!#
&*
!’
!!
!$
&)
!”

recast

α = .&%
Forecast

α = .)%
Forecast

—
!%
!#.)
!#.*%
!#.+&
!#.”
!#.&*
!#.)$
!%.”+
!%.&$
!#.*%
!#.+&

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!%
!#.%
!#.*%
!#.#$
!#.”*
!”.%$
!%.$$
!&.#&
!&.))
!#.$&
!”.*%

Actual
45

α = .4

Demand

α = .1

40

0

2

4

6

8

10

12

Period

Selecting a smoothing constant is basically a matter of judgment or trial and error, using
forecast errors to guide the decision. The goal is to select a smoothing constant that balances
the benefits of smoothing random variations with the benefits of responding to real changes if
and when they occur. Commonly used values of ! range from .05 to .50. Low values of ! are
used when the underlying average tends to be stable; higher values are used when the underlying average is susceptible to change.
Some computer packages include a feature that permits automatic modification of the
smoothing constant if the forecast errors become unacceptably large.
Exponential smoothing is one of the most widely used techniques in forecasting, partly
because of its ease of calculation and partly because of the ease with which the weighting
scheme can be altered—simply by changing the value of !.
Note: Exponential smoothing should begin several periods back to enable forecasts to adjust
to the data, instead of starting one period back. A number of different approaches can be
used to obtain a starting forecast, such as the average of the first several periods, a subjective
estimate, or the first actual value as the forecast for period 2 (i.e., the naive approach). For
simplicity, the naive approach is used in this book. In practice, using an average of, say, the
first three values as a forecast for period 4 would provide a better starting forecast because that
would tend to be more representative.

Other Forecasting Methods
Focus forecasting Using
the forecasting method that
demonstrates the best recent
success.

ste3889X_ch03_074-137.indd 88

You may find two other approaches to forecasting interesting. They are briefly described in
this section.

Focus Forecasting Some companies use forecasts based on a “best recent performance” basis. This approach, called focus forecasting, was developed by Bernard T. Smith,

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Chapter Three Forecasting
y

#$

FIGURE #.&

y

Graphs of some nonlinear
trends
Parabolic
trend

Life cycle
trend

Time

Time
y

y

Growth
curve

Exponential
trend

Time

Time

and is described in several of his books.1 It involves the use of several forecasting methods
(e.g.,! moving average, weighted average, and exponential smoothing) all being applied to
the last few months of historical data after any irregular variations have been removed. The
method that has the highest accuracy is then used to make the forecast for the next month.
This process is used for each product or service, and is repeated monthly.

Diffusion Models When new products or services are introduced, historical data are not
generally available on which to base forecasts. Instead, predictions are based on rates of product adoption and usage spread from other established products, using mathematical diffusion
models. These models take into account such factors as market potential, attention from mass
media, and word of mouth. Although the details are beyond the scope of this text, it is important to point out that diffusion models are widely used in marketing and to assess the merits
of investing in new technologies.

Techniques for Trend
Analysis of trend involves developing an equation that will suitably describe trend (assuming
that trend is present in the data). The trend component may be linear, or it may not. Some
commonly encountered nonlinear trend types are illustrated in Figure 3.5. A simple plot of the
data often can reveal the existence and nature of a trend. The discussion here focuses exclusively on linear trends because these are fairly common.
There are two important techniques that can be used to develop forecasts when trend
is present. One involves use of a trend equation; the other is an extension of exponential
smoothing.

Trend Equation A linear trend equation has the form
Ft = a + bt

(3–4)

Linear trend equation Ft =
a + bt, used to develop forecasts when trend is present.

where
Ft = Forecast for period t
a = Value of Ft at t = 0, which is the y intercept
b = Slope of the line
t = Specified number of time periods from t = 0

LO3.10 Prepare a linear
trend forecast.

1
See, for example, Bernard T. Smith and Virginia Brice, Focus Forecasting: Computer Techniques for Inventory
Control Revised for the Twenty-First Century (Essex Junction, VT: Oliver Wight, 1984).

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Chapter Three Forecasting

$%

y

Ft = a

Δy
Δt

a

+ bt

b=

Δy
Δt

0

t

For example, consider the trend equation Ft = 45 + 5t. The value of Ft when t = 0 is 45,
and the slope of the line is 5, which means that, on average, the value of Ft will increase by
five units for each time period. If t = 10, the forecast, Ft, is 45 + 5(10) = 95 units. The equation can be plotted by finding two points on the line. One can be found by substituting some
value of t into the equation (e.g., t = 10) and then solving for Ft. The other point is a (i.e., Ft at
t = 0). Plotting those two points and drawing a line through them yields a graph of the linear
trend line.
The coefficients of the line, a and b, are based on the following two equations:
n∑ ty ” ∑ t∑ y
b = _____________
n∑ t 2 ” (∑ t) 2

(3–5)

∑ y ” b∑ t
a = _________!or!y¯ ” b¯t
n

(3–6)

where
n = Number of periods
y = Value of the time series
Note that these two equations are identical to those used for computing a linear regression
line, except that t replaces x in the equations. Values for the trend equation can be obtained
easily by using the Excel template.

EXAMPLE

#

mhhe.com/stevenson14e

ste3889X_ch03_074-137.indd 90

Obtaining and Using a Trend Equation
Cell phone sales for a California-based firm over the last 10 weeks are shown in the following table. Plot the data and visually check to see if a linear trend line would be appropriate.
Then, determine the equation of the trend line, and predict sales for weeks 11 and 12.
Week

Unit Sales

#
%
&
!
$
‘
+
)
*
#”

+””
+%!
+%”
+%)
+!”
+!%
+$)
+$”
++”
++$

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Chapter Three Forecasting

a.

$&

S O L U T I O N

A plot suggests that a linear trend line would be appropriate:
780

Sales

760
740
720
700
1

2

3

4

5

6

7

8

9

10

11 12

Week

b.

The solution obtained by using the Excel template for linear trend is shown in
Table!3.1.
b = 7.51 and a = 699.40
The trend line is Ft = 699.40 + 7.51t, where t = 0 for period 0.

c.

Substituting values of t into this equation, the forecasts for the next two periods (i.e.,
t!= 11 and t = 12) are:
F11 = 699.40 + 7.51(11) = 782.01
F12 = 699.40 + 7.51(12) = 789.52

d.

For purposes of illustration, the original data, the trend line, and the two projections
(forecasts) are shown on the following graph:
800
Forecasts
780

Sales

760
740

Data

Trend line

720
700
1

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91

2

3

4

5

6 7
Week

8

9

10 11 12

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$’

Chapter Three Forecasting

TABLE #.$ Excel solution for Example ”

Source: Microsoft

Trend-Adjusted Exponential Smoothing
Trend-adjusted exponential
smoothing Variation of exponential smoothing used when
a time series exhibits a linear
trend.
LO3.11 Prepare a trendadjusted exponential
smoothing forecast.

A variation of simple exponential smoothing can be used when a time series exhibits a linear
trend. It is called trend-adjusted exponential smoothing, or sometimes double smoothing,
to differentiate it from simple exponential smoothing, which is appropriate only when data
vary around an average or have step or gradual changes. If a series exhibits a trend, and simple
smoothing is used on it, the forecasts will all lag the trend: If the data are increasing, each
forecast will be too low; if decreasing, each forecast will be too high.
The trend-adjusted forecast (TAF) is composed of two elements—a smoothed error and a
trend factor.
TAF t+1 = St + T t

(3–7)

where
St = Previous forecast plus smoothed error
Tt = Current trend estimate
and
St = TAF t + !(At ” TAF t)
Tt = Tt”1 + “(TAF t ” TAF t”1 ” Tt”1)

(3–8)

where
! = Smoothing constant for average
” = Smoothing constant for trend
In order to use this method, one must select values of ! and ” (usually through trial and
error) and make a starting forecast and an estimate of trend.
Using the cell phone data from the previous example (where it was concluded that the data
exhibited a linear trend), use trend-adjusted exponential smoothing to obtain forecasts for
periods 6 through 11, with ! = .40 and ” = .30.

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Chapter Three Forecasting

$(

TABLE #.% Using the Excel template for trend-adjusted smoothing

Source: Microsoft

The initial estimate of trend is based on the net change of 28 for the three changes from
period 1 to period 4, for an average of 9.33. The Excel spreadsheet is shown in Table 3.2.
Notice that an initial estimate of trend is estimated from the first four values and that the starting forecast (period 5) is developed using the previous (period 4) value of 728 plus the initial
trend estimate:
Starting!forecast = 728 + 9.33 = 737.33
Unlike a linear trend line, trend-adjusted smoothing has the ability to adjust to changes
in trend. Of course, trend projections are much simpler with a trend line than with trendadjusted forecasts, so a manager must decide which benefits are most important when choosing between these two techniques for trend.

Techniques for Seasonality
Seasonal variations in time-series data are regularly repeating upward or downward movements in series values that can be tied to recurring events. Seasonality may refer to regular annual variations. Familiar examples of seasonality are weather variations (e.g., sales of
winter and summer sports equipment) and vacations or holidays (e.g., airline travel, greeting
card sales, visitors at tourist and resort centers). The term seasonal variation is also applied
to daily, weekly, monthly, and other regularly recurring patterns in data. For example, rush
hour traffic occurs twice a day—incoming in the morning and outgoing in the late afternoon. Theaters and restaurants often experience weekly demand patterns, with demand
higher later in the week. Banks may experience daily seasonal variations (heavier traffic during the noon hour and just before closing), weekly variations (heavier toward the end of the
week), and monthly variations (heaviest around the beginning of the month because of Social
Security, payroll, and welfare checks being cashed or deposited). Mail volume; sales of toys,
beer,!automobiles, and turkeys; highway usage; hotel registrations; and gardening also exhibit
seasonal variations.

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93

Seasonal variations Regularly repeating movements in
series values that can be tied
to recurring events.

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$)

Punchstock/Getty Images

Seasonal relative Percentage
of average or trend.

FIGURE #.’

Seasonality: the additive
and multiplicative models
compared using a linear
trend

Chapter Three Forecasting

Seasonality in a time series is
expressed in terms of the amount
that actual values deviate from
the average value of a series. If
the series tends to vary around an
average value, then seasonality is
expressed in terms of that average
(or a moving average); if trend is
present, seasonality is expressed
in terms of the trend value.
There are two different models of seasonality: additive and
multiplicative. In the additive
model, seasonality is expressed
as a quantity (e.g., 20 units),
which is added to or subtracted
from the series average in order
to incorporate seasonality. In!the
multiplicative model, seasonality is expressed as a percentage of the average (or trend)
amount (e.g., 1.10), which is
then used to multiply the value
Steve Mason/Getty Images
of a series to incorporate seasonality. Figure!3.6 illustrates the two models for a linear trend line. In practice, businesses use the
multiplicative model much more widely than the additive model, because it tends to be more
representative of actual experience, so we will focus exclusively on the multiplicative model.
The seasonal percentages in the multiplicative model are referred to as seasonal relatives
or seasonal indexes. Suppose that the seasonal relative for the quantity of toys sold in May at
a store is 1.20. This indicates that toy sales for that month are 20 percent above the monthly
average. A seasonal relative of .90 for July indicates that July sales are 90 percent of the
monthly average.
Knowledge of seasonal variations is an important factor in retail planning and scheduling.
Moreover, seasonality can be an important factor in capacity planning for systems that must
be designed to handle peak loads (e.g., public transportation, electric power plants, highways,
and bridges). Knowledge of the extent of seasonality in a time series can enable one to remove
seasonality from the data (i.e., to seasonally adjust data) in order to discern other patterns

Demand

Additive model
Demand = Trend + Seasonality

Multiplicative model
Demand = Trend × Seasonality
Time

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Chapter Three Forecasting

$*

or the lack of patterns in the series. Thus, one frequently reads or hears about “seasonally
adjusted unemployment” and “seasonally adjusted personal income.”
The next section briefly describes how seasonal relatives are used.

Using Seasonal Relatives Seasonal relatives are used in two different ways in forecasting.
One way is to deseasonalize data; the other way is to incorporate seasonality in a forecast.
To deseasonalize data is to remove the seasonal component from the data in order to
get a clearer picture of the nonseasonal (e.g., trend) components. Deseasonalizing data is
accomplished by dividing each data point by its corresponding seasonal relative (e.g., divide
November demand by the November relative, divide December demand by the December
relative, and so on).
Incorporating seasonality in a forecast is useful when demand has both trend (or average)
and seasonal components. Incorporating seasonality can be accomplished in this way:
1.

Obtain trend estimates for desired periods using a trend equation.

2.

Add seasonality to the trend estimates by multiplying (assuming a multiplicative model
is appropriate) these trend estimates by the corresponding seasonal relative (e.g., multiply the November trend estimate by the November seasonal relative, multiply the
December trend estimate by the December seasonal relative, and so on).

LO3.12 Compute and use
seasonal relatives.

Example 4 illustrates these two techniques.

a. Deseasonalizing Data and
b. Using Trend and Seasonal Relatives to make a Forecast
A coffee shop owner wants to estimate demand for the next two quarters for hot chocolate.
Sales data consist of trend and seasonality.
a.

b.

a.

b.

EXAMPLE

”

mhhe.com/stevenson14e

Quarter relatives are 1.20 for the first quarter, 1.10 for the second quarter, 0.75 for the
third quarter, and 0.95 for the fourth quarter. Use this information to deseasonalize
sales for quarters 1 through 8.
Using the appropriate values of quarter relatives and the equation Ft = 124 + 7.5t for
the trend component, estimate demand for periods 9 and 10.

Period
#
%
&
!
$
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+
)

Quarter
#
%
&
!
#
%
&
!

Sales
(gal.)
#$).!(
#$&.”(
##”.”(
#!’.&(
#*%.”(
#)+.”(
#&%.”(
#+&.)(

÷
÷
÷
÷
÷
÷
÷
÷
÷

Quarter
Relative
#.%”(
#.#”(
“.+$(
“.*$(
#.%”(
#.#”(
“.+$(
“.*$(

=
=
=
=
=
=
=
=
=

Deseasonalized
Sales
#&%.”(
#&*.#(
#!’.+(
#$!.”(
#'”.”(
#+”.”(
#+’.”(
#)%.*

S O L U T I O N

The trend values are:
Period 9: Ft = 124 + 7.5(9) = 191.5
Period 10: Ft = 124 + 7.5(10) = 199.0
Period 9 is a first quarter and period 10 is a second quarter. Multiplying each trend
value by the appropriate quarter relative results in:
Period 9: 191.5(1.20) = 229.8
Period 10: 199.0(1.10) = 218.9

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Chapter Three Forecasting

$”

FIGURE #.!

50

A centered moving
average closely tracks the
data

Data

Demand

40

Centered
MA

30

20

0

Centered moving average A
moving average positioned
at the center of the data that
were used to compute it.

5

10

15
Period

20

25

30

Computing Seasonal Relatives A widely used method for computing seasonal relatives
involves the use of a centered moving average. This approach effectively accounts for any trend
(linear or curvilinear) that might be present in the data. For example, Figure 3.7 illustrates how
a three-period centered moving average closely tracks the data originally shown in Figure 3.3.
Manual computation of seasonal relatives using the centered moving average method is a bit
cumbersome, so the use of software is recommended. Manual computation is illustrated in Solved
Problem 4 at the end of the chapter. The Excel template (on the website) is a simple and convenient
way to obtain values of seasonal relatives (indexes). Example!5 illustrates this approach.
For practical purposes, you can round the relatives to two decimal places. Thus, the seasonal (standard) index values are:
Day
Tues

Index
“.)+(

Wed
Thurs
Fri
Sat
Sun
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Computing Seasonal Relatives Using the Simple Average Method The simple average (SA) method is an alternative way to compute seasonal relatives. Each seasonal relative is
the average for that season divided by the average of all seasons. This method is illustrated in
Example 5, where the seasons are days. Note that there is no need to standardize the relatives
when using the SA method.

EXAMPLE

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mhhe.com/stevenson14e

Computing Seasonal Relatives
The manager of a call center recorded the volume of calls received between 9 and 10 a.m.
for 21 days and wants to obtain a seasonal index for each day for that hour.
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11/29/19 03:42 PM

Final PDF to printer

Chapter Three Forecasting

Compute Seasonal Indexes

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