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Forecasting

Chapter outline

11.1 Forecasting for decision making

11.2 Qualitative forecasting methods

11.3 Time-series forecasting

11.4 Moving average

11.5 Exponential smoothing

11.6 Forecast accuracy

11.7 Advanced time-series forecasting

11.8 Causal forecasting methods

11 .9 Selecting a forecasting method

11 .10 Collaborative planning, forecasting, and replenishment

11 .11 Key points and terms

Forecasting is the art and science of predicting future events. In organizations, managers are usually most interested in predicting future demand. Before appro- priate software was available, forecasting was largely an art, but it has more re- cently developed into a science as well. Although managerial judgment is s till required for forecasting, managers today are aided by both simple and sophisti- cated mathematical tools and methods, as well as significant amounts of data from a wide variety of sources. For example, airlines forecast future capacity needs by analyzing their own historical demand data as well as data on the pricing and capacity of their competitors. Forecasting has indeed come a long way from the black art of fortune-telling by use of the stars, tea leaves, or crystal balls.

Many different methods of forecasting and their u ses are described here. Select- ing the best forecasting method for a given situation must be done carefully for the particular use it is intended to serve. There is no universal forecasting method for all situations.

Forecasts will almost always be wrong. It is rare for sales to equal the exact amount forecast. A little variation from the forecast can often be absorbed by extra capacity, inventory, or rescheduling of orders. But large variations can wreak havoc in the business. For example, suppose 100,000 cases of a product are fore- cast to be sold in a particular year, and only 80,000 cases are actually sold. The extra 20,000 cases can end up in inventory, or perhaps employment might be cut to reduce production levels. It is equally painful if the forecast is too low. Then

251

252 Part Four Capacity and Scheduling

Operations Leader A Winning Forecast for H arrah's Cherokee Casino & Hotel

Harrah's Cherokee Casino & Hotel, located in the town of Cherokee, North Carolina, draws about four million visitors each year. Its alcohol-free facilities include 576 hotel rooms and 3400 gaming devices (such as elec- tronic blackj ack and baccarat), along wit h several res- taurants and meeting rooms . The Eastern Band of Cherokee Indians contracts w ith Harrah's, the world's largest gaming company, to manage the casino an d hotel. Profits are used to support health care, educa- tion, and other initiatives for the local Native American comm unity.

Sophisticated segmentation of customers, analysis of past demand patterns, and focused pricing strategies

have helped Cherokee achieve an annua l occupancy rate of 98.6 percent. And most of their customers drive f rom Atlanta, Georgia-three hours away ! How do they do it?

Cherokee first determines true customer demand for its service, based on past demand and reserva- tion requests that were denied (because facilities were full) . True customer demand is often greater than realized demand (i.e., sales) due to t he reserva- tion denials. Customers provide their casino mem- bersh ip number when requesting reservations, making it easy for Cherokee to track both accepted and denied reservation requests.

Next, Cherokee develops its daily forecast based on historical data. For example, the forecast for a particular Saturday might be based on demand for recent Saturdays as well as simila r dates in previous years. The forecast model accounts for day of week, seasonality, trends, and other special-event factors.

Based on its fore) ast and know ledge about the price each customer segment is willing to pay for a hotel room, Cherokee sets a room price for each cus- tom er segment on each day. This enables manage- ment to maximize the price of every room on every day, resulting in a 60 percent profit margin.

Source: Metters et al., " The 'Killer Application' of Revenue Management: Harrah's Cherokee Casino & Hotel," Interfaces, May-June 2008.

capacity is strained , extra w orkers m ay be added in a rush, or sales may be lost due to stockouts. From these examples it is clear that forecasting h as a strong impact on operations an d, indeed , all functions in the business.

Given the challen ge of getting the forecast " right," there are three m ain ways for man agers to accom modate forecasting errors. One is to try to reduce the error throu gh better for ecasting. The second is to b uild m ore flexibility into operations and the sup ply chain. The third is to reduce the lead time ov er which forecasts are required . This is because forecasting error u sually increases as the forecasting time h orizon increases, so next week's fo recast w ill u sually h av e less error than next m onth's forecast. Even good forecasts w ill h ave some error, but the lowest possi- ble error alon g w ith reason able forecasting costs is the goal.

In recognition of inherent forecastin g error, all forecasts should h ave at least two numbers: one for the b est estimate of dem and (e.g., mean, median, or mode) and the other for forecastin g error (st andard deviation, absolute d eviation, or range). To produce forecasts with only an average is to ignore error, but this is a common occurrence in practice.

Forecasting problems are often very complex and difficult. One examp le is fore- casting the 50,000 d ifferent item s carried b y a typical grocery store. Stockout of a

Chapter 11 Forecasting 253

particular brand or size of package can cause a loss of sales for both the retailer and the producer. Thus, forecasting occupies a central role in the firm, and all along the supply chain, because of its complexity and its impact on the business. Harrah's Cherokee Casino & Hotel performs complex forecasting for its service, as described in the Operations Leader box.

11.1 FORECASTING FOR DECISION MAKING

Although there are many types of forecasting, this chapter will focus on forecasting demand for output from the operations function. Demand and sales, however, are not always the same thing. Whenever the demand is not constrained by capacity or other management policies, the forecasting of demand will be the same as the fore- casting of sales. Otherwise, sales may be somewhat below real customer demand.

We should also clarify the difference between forecasting and planning. Fore- casting deals with what we think will happen in the future. Planning deals with what we think should happen in the future. Thus, through planning, we con- sciously attempt to alter future events, while we use forecasting only to predict them. Good planning utilizes a forecast as an input. If the forecast is not accept- able, sometimes a plan can be devised to change the course of events.

Forecasting is one input to all types of business planning and control, both in- side and outside the operations function. Marketing uses forecasts for planning products and services, promotion, and pricing. Finance uses forecasting as an in- put to financial planning. Forecasting is an input for operations decisions on pro- cess design, capacity planning, and inventory.

For process design purposes, forecasting is needed to decide on the type of pro- cess and the degree of automation to be used. For example, a low forecast of future

• demand may indicate that little automation is needed and the process should be kept as simple as possible. If greater volume is forecast, more au- tomation and a more elaborate process, including assembly-line flow, may be justified. Since process decisions are long range in nature, they can re- quire forecasts for many years into the future.

Operations, Marketing, Finance, and Human Resources mllaborate to both create and use forecasts.

Capacity decisions utilize forecasts at several different levels of aggregation and precision. For planning the total capacity of facilities, a long- range forecast several years into the future is needed. For medium-range capacity decisions ex- tending through the next year or so, a more de- tailed forecast by product line or service will be needed to determine hiring plans, subcontracting, and equipment decisions. Besides being more de-

"Service Processing at BuyCostumes

.com," Vol. XIII

tailed, the medium-range forecast should be more accurate, if possible, than the long-range forecast. Short-range capacity decisions, including the assignment of available workers and machines to jobs or activities in the near future, should be detailed in terms of individual products or services. The forecast used to guide these short-range decisions should be highly accurate.

Inventory decisions resulting in purchasing actions tend to be short range in nature and deal with specific products. The forecasts that lead to these decisions must meet the same requirements as short-range scheduling forecasts: They must

2 54 Part Four Capacity and Scheduling

TABLE 11 .1

have a high degree of accuracy and individual product specificity. For inventoty and scheduling decisions, because of the many items usually involved, it is also necessary to produce a large number of forecasts. Thus, a computerized forecast- ing system often is used for these decisions.

Forecasting is used for many purposes in marketing, including sales planning. new-product and new-service introduction, design of marketing programs, pric- ing decisions, advertising, and distribution planning. Forecasting isn't limited to one aspect of marketing; rather, it affects all marketing decisions. In fact, fore- casting responsibility may sometimes be assigned to marketing or to a cros5- functional team consisting of marketing, operations, and finance personnel.

The finance, accounting, and human resources functions are also keenly interested in forecasting. Even the routine task of making a budget or estimating costs requires a volume forecast and financial plans grounded on forecasts of sales. Human re- sources requires a forecast to anticipate hiring decisions and personnel budgets.

In summary, there are different types of decisions in operations and different forecasting requirements, as shown in Table 11.1. The table also shows some of the decisions in marketing, finance / accounting, and human resources that require a forecast. And it indicates the three types of forecasting methods associated with these decisions: qualitative, time series, and causal.

In general terms, qualitative forecasting methods rely on managerial judg- ment; they do not use specific quantitative models. Qualitative methods are useful when there is a lack of data or when past data are not reliable predictors of the future. In this case, the human decision maker can utilize the best available data and a qualitative approach to arrive at a forecast. •

There are two general types of quantitative forecasting methods: time-series and causal forecasting. Quantitative methods utilize an underlying mathematical model to arrive at a forecast . The basic assumption for all quantitative forecasting methods is that past data and data patterns are reliable predictors of the future. Past data are then analyzed in a time-series or causal model to arrive at a forecast.

In the remainder of this chapter, we will be referring to long, medium, and short time ranges. "Long range" will mean two years or more into the future, a

Forecasting Uses and Methods

Time Horizon

Uses of Forecasting for Operations Decisions

Process design Long Capacity planning faci lities Long Aggregate planning M edium Scheduling Short Inventory management Short

Accuracy Required

Medium M edium High Hig hest Highest

Number of Forecasts

Single or few Single or few Few Many Many

Uses of Forecasting in Marketing, Finance, and Human Resources

Long-range marketing programs Long Medium Single or few Pricing decisions Short High Many New-product introduction Medium Medium Single Cost estimating Short High Many Capital budgeting Medium High Few Labor planning Medium Medium Few

Management Level

Top Top Middle Lower Lower

Top Middle Top Lower Top Lower

Forecasting Method

Qualitative or causal Qualitative and causal Causal and time series Time series Time series

Qualitative Time series Qualitative and causal Time series Ca usal and t ime series Qualitative and time series

Chapter 11 Forecasting 255

common horizon for the planning of facilities and processes. "Medium range" is defined as between six months and two years, the normal time frame for aggre- gate planning decisions, budgeting, and other resource acquisition and allocation decisions. "Short range" will refer to less than six months, where the decisions in- volve procurement of materials and scheduling of particular jobs and activities. For short-range decisions, forecasts that extend through procurement or produc- tion lead times are sufficient.

11.2 QUALITATIVE FORECASTING METHODS

Qualitative forecasting methods utilize managerial judgment, experience, relevant data, and an implicit mathematical model. Because the model is implicit, two dif- ferent managers both using qualitative methods often arrive at widely different forecasts.

Some people think that qualitative forecasts should be used only as a last resort. This is not strictly true. Qualitative forecasts should be used when past data are not reliable indicators of future conditions. When this happens, past data must be tempered by judgment before a forecast can be developed. Qualitative forecasting must also be used for new-product and new-service introductions for which his- torical demand data are not available. In these cases, qualitative methods can be used to develop a forecast by analogy or by the selective use of market research data. Note, a systematic approach to qualitative forecasting is possible even though an explicit mathematical model is not formulated.

Table 11.2 describes four of the best-known qualitative methods and some of the characteristics of each one. As can be seen, qualitative methods typically are used for ,medium- and long-range forecasting involving process design or theca- pacity of facilities. For these decisions, past data are not usually available or, if they are, may show an unstable pattern.

Both informed judgment and the Delphi method use expert opinion to arrive at a forecast. When informed judgment is used with a panel, the group will discuss the forecast and arrive at a consensus. The danger of this method is that some- times not all members of the panel are heard, there can be a rush to make a deci- sion and one person can dominate the panel in terms of the final judgment.

The Delphi method was developed to correct this situation. It consists of sev- eral rounds of anonymous data collection before reaching a forecast. In the first round of the Delphi method each member of the panel anonymously provides his or her forecast. Then the forecast information from all panel members is fed back to each panel member, again anonymously, along with any reasons or comments about their forecasts. In the second and subsequent rounds m embers can review the forecasts of the other panel members and then revise their forecasts if they find n ew information. After three or four rounds of data collection, there is a tendency for the forecast to converge to a range of forecast values, and members no longer adjust their forecasts qn the basis of panel feedback. As a result, the Delphi panel arrives not only at a most likely forecast (e.g., mean, median, or mode) but also an estimate of forecast error (e.g., standard deviation, absolute deviation, or range).

Market surveys are commonly used to get information from potential customers about willingness to buy a product or service. A variety of m ethods can be used, including customer responses via phone, mail, or Internet. Also, test markets are an effective way to gauge customer demand. They may be more accurate than market surveys since customers actually buy the product or service in a test market.

"' Ul en

TABLE 11.2 Qualitative Forecasting Methods

Qualitative Methods

1. Delphi

2. Market surveys

3. Life-cycles analogy

4. Informed judgment

Description of Method

Forecast developed by a panel of experts answering a series of questions on successive rounds. Anonymous responses of the panel are fed back on each round to all participants. Three t o six rounds may be used to obt ain convergence of the forecast.

Panels, question naires, test markets, or surveys used to gather dat a on market condit ions.

Prediction based on t he introduc- tion, growth, and maturity phases of similar p roducts. Uses the S-shaped sales growth curve.

Forecast may be made by a group or an individual on the basis of experience, hunches, or facts about the situation. No rigorous method is used.

Uses

Long-range sales forecasts for capacity or facility planning. Technological forecasting to assess when technological changes might occur.

Forecasts of t otal company sales, major product groups, or individual products.

Fo recasts of long-range sales fo r capacity or f acility planning.

Forecasts for total sales and individual products.

Short Term

Fair to very good

Very good

Poor

Poor to fa ir

Accuracy

Identif ication Medium Long of Turning Relative

Term Term Point Cost

Fair to very Fair to very Fair to good Medium good good to high

Good Fair Fair to good High

Fair to good Fair to good Poor to fa ir Medium

Poor to fai r Poor to fair Poor to fair Low

Source: Reprinted by permission of the Harvard Busiuess Review. Exhibit adapted from David M . Georgoff and Robert Murdick, "Manager 's Guide to Forecasting," Harvard Business Review, january-February 1986, pp. 11(}-120.

Chapter 11 Forecasting 257

Another method, used especially for forecasts of new products, is the life-cycle analogy. This method is based on the idea that product or service demand has well-defined life stages (introduction, growth, and maturity) that follow an S-shaped curve. To gauge the shape of the curve, an analogy with a similar prod- uct or service is used. For example, an estimate of demand for a new website is based on the actual growth curve of similar websites that is derived from the demand they generated over time.

Although we are not describing qualitative methods in detail we note their usefulness in certain situations. Next, we turn to the first type of quantitative model: time-series methods, which are well suited to multiple forecasts of a short- range nature.

11.3 TIME-SERIES FORECASTING

Time-series methods are used to make detailed analyses of past demand patterns over time and use those patterns to predict demand in the future. One of the basic assumptions of all time-series methods is that demand can be decomposed into components such as average level, trend, seasonality, cycle, and random error. A

Snow skiing is an industry that exhibits several demand patterns. It is primarily a seasonal (i.e., winter) industry, and over many years the industry has experienced a growth trend. Random factors like snowfall cause variations, or abrupt peaks and valleys, in demand.

AGURE 11.1 Decomposition of time-series data.

"'tl c a E D ....

Time

Original Time Series (Real Demand)

1 Green et al. (2007).

.., ; s "' 0

sample of these components for a representative time series is shown in Figure 11.1. When the com- ponents are added together (or in some cases mul- tiplied), they will equal the original time series.

The level is the relatively constant average de- mand during a time interval. The trend is an in- crease or decrease in the average demand over time. Seasonality is a regularly repeated pattern of increasing and decreasing demand. It can be a yearly pattern (such as peak demand at the book- store at the start of each semester), but can also ap- ply to shorter time frames. For example, a 24-hour financial services call center experiences a seasonal d emand pattern on a daily basis. Peak d emand oc- curs between 8 a.m. and 3 p.m., moderate demand 5 a.m.- 8 a.m. and 3 p .m.-10 p.m., and very little d emand during other times.l The cycle is increas- ing or decreasing demand over long time periods,

Cycle

Seasonality

---------------------------- Trend -------------- Level

Vf'-Nnll Random error

Time

258 Part Four Capacity and Scheduling

often many years. Cyclical changes in demand may be due to changes in the oveP< all economy or changes in product or service life cycles, among other reasons Random error reflects short-term fluctuations in demand that cannot be forecast.

The basic strategy used in time-series forecasting is to identify the magnitucll and form of each component on t~e basis of available past data. These compo4 nents, except the random error component, are then used to estimate future de- mand in the form of a forecast.

In discussions of time-series forecasting, the following symbols and terminoiJ ogy are used:

Observed Demands

Data

Period

Present Time

Dt = demand during period t Ft+ 1 = forecast demand for period t + 1

et = D 1

- Ft =forecast error in period t A t = average computed through period t

Forecasts at Time t

We are at the end of period t, having just observed actual demand that defines the value of 0

1 , and are making forecasts for future periods t + 1, t + 2, t + 3, and so on.

11.4 MOVING AVERAGE

The simplest method of time-series forecasting is the moving-average method. For this method, it is assumed that the time series has only a level component plus a random error component. No seasonal pattern, trend, or cycle components are assumed to be present in the demand data. More advanced versions of the moving average can, however, include these additional components.

When the moving average is used, a given number of periods (N) is selected for the computations. Then the average dem and, A

1 , for the past N periods at time tis

computed as follows:

(11.1)

Since we are assuming that the time series is level (or horizontal), the best forecast for period t + 1 is simply the average demand observed through period t. Thus, we have

Ft+l =At

Each time Ft + 1 is computed , the most recent periods of demand are included in the calculation of the average and the older p eriods of demand are dropped. This p rocedure maintains N periods of demand in the forecast and lets the average move along as new d emand d ata are observed.

In Table 11.3, a three-period moving average is u sed for forecasting purposes. Notice how the moving average is offset by one period to obtain the moving fore- cast. The forecast error is also shown in the table as the differen ce between actual and forecast d emand. Always use the forecast for period t (F

1 ) in computing fore-

cast errors, not the average for period t (A 1 ).

TABLE 11.3 M oving-Average Forecasts

R GURE 11.2 )ime-series data.

Chapter 11 Forecasting 259

At Ft D, (Three-Period (Three-Period D,-F,

Period (Demand) Moving Average) Forecast) (Error)

10~ 2 18 3 29 19.0~ 4 15 20.7--------...19.0 -4.0 5 30 24.7 . .. 20.7 +9.3 6 12 19.0 24.7 - 12.7 7 16 19.3 19.0 -3.0 8 8 12 .0 19.3 -1 1.3 9 22 15.3 12.0 10.0

10 14 14.7 15.3 -1.3 11 15 17.0 14. 7 0.3 12 27 18.7 17.0 10.0 13 30 24.0 18.7 1 1.3 14 23 26. 7 24.0 - 1.0 15 15 22 .7 26.7 - 11.7

Let's calculate some of the numbers in Table 11.3 for illustrative purposes, start- ing with period 3. Since we are using a three-period moving average, A 3 is just the sum of demands from periods 3, 2, and 1 averaged over these three periods:

A 3

= (29 + 18 + 10)/3 = 19

The forecast for period 4 is equal to the moving average through period 3; there- fore, F

4 = 19. After we see the actual demand in period 4, which turns out to be

D 4

= 15, we can' calculate a forecast error as follows:

et = Dt - Ft

The forecast error in period 4 is 15 - 19 = 4. Check some of the numbers in this table for yourself to make sure you understand the calculations.

The graph in Figure 11.2 shows the demand data from the example, the three- period moving average, and a six-period moving average. The six-period moving averages are: A

6 = 19.0, A

7 = 20.0, A

8 = 18.3, A

9 = 17.2, and so forth. It is a good

idea to plot the data and forecasts when making comparisons. Notice how the

0 2 4 6 8 Time period

10 12 14

260 Part Four Capacity and Scheduling

six-period moving average responds more slowly to demand changes than does the three-period moving average. As a general rule, the longer the averaging pe- riod, the slower the response to demand changes. A longer period thus has thr advantage of providing stability in the forecast but the disadvantage of respord ing more slowly to real changes in the demand level. The forecasting analyst must select the appropriate trade-off between stability and response time when select- ing the number of periods in N.

One way to make the moving average respond more rapidly to changes in demand is to place relatively more weight on recent demands than on earlier ones. This is called a weighted moving average, which is computed as follows:

Ft+ 1 =At = W1Dt + W2Dt- 1 + .. . + W NDt-N+ 1 with the condition

i= l

(11 .2]

In a weighted moving average, any desired weights can be specified so long as they add up to 1. For example, if we have demands D1 = 10, D2 = 18, and D

3 = 29, the ordinary three-period moving average is 19.0. With weights of

wl = .5, w2 = .3, and w3 = .2, the three-period weighted moving average is 21.9. In this case, the weight of .5 was applied to the third period, .3 to the second p e- riod, and .2 to the first period. Notice, for this example, how the weighted mov- ing average has responded more rapidly than the ordinary moving average to the increased demand of 29 in the third period. Notice also that the simple moving average is just a special case of the weighted moving average with all w eights equal, W; = 1/N.

One of the disadvantages of a weighted moving average is that the entire de- mand history for N periods must be carried along with the computation. Further- more, the responsiveness of a weighted moving average cannot be changed easily without changing each of the weights. To overcome these difficulties, the method of exponential smoothing has been developed.

11.5 EXPONENTIAL SMOOTHING

Exponential smoothing is based on the simple idea that a new average can be computed from an old average along with the most recent observed demand. Sup- pose, for example, we hav e an old average of 20 and we have just observed a de- mand of 24. The new av erage will lie between 20 and 24, depending on how m uch w eight we want to assign to the demand just observed versus the weight on the old average.

To formalize the above logic, w e can write

(11.3)

In this case, A t-1 is the old average (20), D 1

the demand just observed (24), and a the proportion of weight placed on the new d em and v ersus the old average (0 ~ a ~ 1). ,

To illustrate, suppose w e use the values a = .1, Dt = 24, and A t _ 1

= 20. Then, from Equation (11.3), w e have At= 20.4. If a = .5, we have A t = 22, and if a = .9, we have A t = 23.6. Thus At varies between the old average of 20 and the demand of 24, depending on the value of a used.

Chapter 11 Forecasting 261

If we want At to be very responsive to recent demand, we should choose a large value of a. If we want At to respond more slowly, a should be smaller. In most fore- casting work, a is given a value between .1 and .3 to maintain reasonable stability.

In simple exponential smoothing, just as in the case of moving averages, we assume that the time series is level with no cycles and that there are no seasonal or trend components. Then the exponentially smoothed forecast for the next period is simply the average obtained through the current period. That is,

Ft + l = At

In this case the forecast is also offset one period from the smoothed average. We can substitute the preceding relationship into Equation (11.3) to obtain the

following equation:

(11.4)

Sometimes this alternative form of simple, or first-order, exponential smoothing is more convenient to use than Equation (11.3) because it uses forecasts instead of averages.

Another way to view exponential smoothing is to rearrange the terms on the right-hand side of Equation (11.4) to yield

Ft +l = Ft + a(Dt - Ft) This form indicates that the new forecast is the old forecast plus a proportion of the error between the observed demand and the old forecast. The proportion of error used can be controlled by the choice of a.

For example, suppose we had forecasted for period 5, F5 = 100, and have just observed the demand for period 5, D5 = 120. In this case we have an error of D

5 - F

5 = 20. If a = .1, then we add only 10 percent of this error to the old forecast

to make the adjustment for the fact that demand has exceeded the forecast. There- fore, the forecast for period 6 is F

6 = 100 + .1 (20) = 102. Note that in using a smooth-

ing constant of .1 we are not overreacting to the fact that we have just observed a demand that exceeded our forecast. However, if we want to react more quickly to demand increases such as this, we could just increase the value of a. For example, what would be the forecast for period 6 if a= .5 or a= .7? (Answer: F

6 = 110 for

a = .5 and F 6

= 114 for a= .7.) Students often ask why the name "exponential smoothing" has been given to

this method. It can be mathematically shown that the weights on each preceding demand data point decrease exponentially, by a factor of (1 - a), until the demand from the first period and the initial forecast F 1 is reached. Since the weights on the previous demands decrease exponentially over time and all the weights add up to 1, exponential smoothing is just a special form of the weighted moving average.

In Table 11.4, two exponentially smoothed forecasts are computed for a = .1 and a = .3, using the same demand data as in Table 11.3. These data are shown graphically in Figure 11.3. As can be seen, the a = .3 forecasts respond more rapidly to demand changes but are less stable than a = .1. Which of these forecasts is better? Remember, we are trying to forecast the average, not the actual shape, of the demand curve.

Before answering this question, we'll look at a few rows in Table 11.4. In row 1 the initial forecast for period 1, F

1 = 15, is given as a starting value. The demand

for period 1 is only 10 units, and so the forecast for period 2 will be decreased. For a= .1 the new forecast F

2 will be 14.5, and for a= .3 the new forecast will be 13.5.

(Practice calculating these numbers yourself.) That is why we say that the forecast

262 Part Four Capacity and Scheduling

TABLE 11.4 Exponential Smoothing*

FIGURE 11.3 Time-series data.

« = .1 «"' .3

D, F, D,-F, F, D,- F, MAD, TS (tracking Period (demand) (forecast) (error) (forecast) (error) (a= .3) signal)

1 10 15 - 5.0 15 - 5.0 6.4 -.8 2 18 14.5 3.5 13.5 4.5 5.8 -.1 3 29 14.85 14.1'5 14.85 14.15 8.3 1.6 4 15 16.26 -1.26 19.09 -4.09 7.1 1.3 5 30 16.14 13.86 17.86 12.14 8.6 2.5 6 12 17.52 -5.52 21.50 -9.50 8.8 1.4 7 16 16.97 -.97 18.65 -2 .65 7.0 1.4 8 8 16.87 -8.87 17.85 - 9.85 7.9 -.1 9 22 15.98 6.02 14.90 7. 10 7.6 .9

10 14 16.58 -2.58 17.03 -3.03 6.2 .6 11 15 16.33 -1.33 16.12 - 1.1 2 4 .7 .6 12 27 16.19 10.81 15.78 11.22 6.7 2.1 13 30 17.27 12.73 19.15 10.85 7.9 3.1 14 23 18.54 4.46 22.40 0.60 5.7 4.4 15 15 18.99 -3.99 22 .58 -7.58 6.4 2.8

2-(Dt - FJ Bias 36.01 17.74 ••• : ~ ... : 2, io, - , Fri Absolute Dev.iation 95 .05 103.38

· ··. - ..

• Assume F1 - 15 as an rubitrary starting point. Also assume MAD0 = 7. See the text for d efinitions of MAD and tracking signaL

reacts more quickly to demand changes for higher values of a but is less stable, since we don't know if the underlying long-term average has changed or whether we are just seeing random fluctuation in the first period.

To answer the question of which is the best forecast, we need to look at forecast errors over many periods. Two measures of forecast accuracy are computed in Table 11.4 for 15 periods. One measure is simply the arithmetic sum of all errors, which reflects the bias in the forecasting method. Ideally, this sum should be zero, since the positive and negative errors should cancel out over time. In Table 11.4, both methods have a positive bias, with a = .1 producing more bias than a = .3.

The second measure of forecast error is the absolute deviation. In this case the absolute values of the errors are summed, so that negative errors do not cancel positive errors. The result is a measure of variance in the forecasting method. The total absolute deviation for a = .1 is less than for a = .3.

Thus, we have the interesting result that the a = .1 forecast has more bias but less absolute deviation than the a = .3 forecast. In this case, there is no clear

40r----,----~-----r----~----~----r----,----~

"" ~ 20~--~r---~+-~,~~--~~~+---+-~~~~--~ ~

Cl

0 2 4 6 8 10 12 14 Time period

Chapter 11 Forecasting 263

preference between the two forecasting models; it depends on the manager 's opinion of the importance of bias and deviation. However, if a forecast has both lower deviation and lower bias, it is clearly preferred.

The procedure for choosing a value of a is now clear. A forecast should be com- puted for several values of a. If one value of a produces a forecast with less bias and less deviation than the others, this value is preferred. If no clear preference exists, trade-offs between bias and deviation must be considered in choosing the preferred value of a.

The exponential smoothing forecast method has the advantage that only one period of demand and forecast data must be carried forward . This significantly simplifies data storage. Unfortunately, simple exponential smoothing cannot al- ways be used in practice because of trends or seasonal effects in the data. When these effects are present, higher-order smoothing, trend-corrected smoothing, or seasonal smoothing may be used. Some of these more advanced methods are pre- sented in the chapter supplement.

11.6 FORECAST ACCURACY

When exponential smoothing is used, an estimate of forecast accuracy should be computed along with the smoothed average. This accuracy estimate might be used for several purposes:

1. To monitor erratic demand observations or outliers, which should be carefully evaluated and perhaps excluded from data analysis.

2. To determine when the forecasting method is no longer tracking actual demand and nefds to be reset.

3. To determine the parameter values (e.g., Nand a) that provide the forecast with the best accuracy.

4. To set safety stocks or safety capacity and thereby ensure a desired level of protection against stockout.

The first three uses will be covered next; the fourth use is covered later in Chapter 15.

There are four different ways to measure the long-run forecast accuracy over several periods. (Recall that e

1 = 0

1 - F

1 is the forecast error for period t, as defined

above.)

Cumulative sum of forecast errors

Mean square error

Mean absolute deviation of forecast errors

Mean absolute percentage errors

1= 1

n

2: e~ MSE = t = l

n n

2: !etl MAD=~

n

~ ~ ~~ 1100 MAPE = ----- (expressed as

n a percentage)

264 Part Four Capacity and Scheduling

Note that n is the number of past periods used to compute the cumulative e~ measurements.

We have already referred to the value of CFE as the bias in the forecast. !dealt the bias will be zero, which occurs if positive errors are offset by negative errors However, if the forecast is always low,. for example, the error will be p ositive each period and the CFE will be a large positive number, indicating a biased fore- cast. In this case the chosen starting point is too low and the forecasting methorl should be reset with a higher starting point.

The second and third formulas measure the variance in the forecast error. 'fbi! square root of MSE is the well-known standard deviation a. MSE uses the squam of each error term so that positive and negative errors do not cancel each othel: out. The other measure of v ariance, MAD, is computed from the absolute valuel of the error in each period instead of the squared errors. MAD is just the averagt! error over n periods without regard to the positive or negative sign of the error in each period. In practice, MAD is widely used in forecasting work because it is easy to understand and easy to use.

The last measure of cumulative forecast error (MAPE) normalizes the error c.ai- culations by computing a percentage error. This will make it possible to compaas forecast errors for different time-series data. For example, if one time series has low demand values and another has much higher demand values, MAPE will be an accurate way of comparing the errors for these two time series.

When exponential smoothing is used, it is commpn to calculate the smoothed! mean absolute deviation period by period, which is defined as follows:

MAD 1 = a!D

1 - F

1 ! + (1 - o:)MAD

1 _ 1

In this case, the new MAD 1 is simply a fraction a of the current absolute deviati(JIIj

plus (1 - o:) times the old MAD. This is analogous to Equation (11.3), since the MAD is being smoothed in the same way as the forecast average. MAD

1 is just an

exponentially weighted average of absolute error terms. The current MAD

1 should be computed for each period along with the forecasl

average. The MAD 1 can then be used to detect an outlier in demand by comparind

the observed deviation with the MADr If the observed deviation is greater thaD 3.75 X MAD

1 , we have reason to suspect that the demand may be an extreme

value. This is comparable to determining whether an observed demand v alue lies outside three standard deviations (a) for the normal dist ribution. This is true because a = 1.25 X MAD

1 for the normal distribution. In Table 11.4, MAD

1 was

computed for a = .3. As can be seen, none of the demand errors fall outside 3.75 X MAD

1 , and so no outliers are suspected in the data.

The second use of MAD 1 is to determine whether the forecast is tracking with the

actual time-series values. To determine this, a tracking signal is computed, as follows:

. . CFE Trackmg s1gnal = TS = MAD

t

The tracking signal is thus a computation of bias (cumulative forecast error) in the numerator divided by the most recent estimate of MADr If demand variations are assumed to b e random, control limits of ±6 on the tracking signal should ensure only a 3 percent probability that the limits w ill b e exce eded by chance.2 Thus

2 These nu merical li mits and probabilities are based on the normal probability dist ribution and a value of ex = .1.

Chapter 11 Forecasting 265

when the tracking signal exceeds ±6, the forecasting method should be stopped and reset to more nearly equal observed demand. In Table 11.4, the tracking signal does not exceed ±6 in any period. Therefore, the forecast is considered to be track- ing sufficiently close to actual demand.

In computerized forecasting systems, it is extremely important to incorporate error controls of the type discussed above. This will ensure that the system does not run out of control. Instead, the user is notified when outliers in demand are detected or when the tracking signal becomes too large.

As an example of these computations, refer to Table 11.4. In the last two columns of the table we have computed smoothed MAD

1 and tracking signal. Starting with

the arbitrary assumption that MAD0 = 7, we can compute MAD1 from the previ- ously given formula as follows using a = .3:

MAD1 = .3[10 - 15[ + .7(7) = 6.4

The tracking signal for period 1 is the cumulative error divided by MAD 1

:

TS = - 5/6.4 = -.8

As an exercise, compute MAD2 and the tracking signal for period 2 and compare your results to Table 11.4.

As we said earlier, forecasting should produce two numbers. The forecast of average demand should be produced along with an estimate of forecasting error. This provides management with more information than a point estimate for deci- sion making. The forecast error forms the basis for understanding the inherent risk in the forecast.

11.7 ADVANCED TIME-SERIES FORECASTING

A variation of exponential smoothing that has received considerable attention is adaptive exponential smoothing. In one form of this approach, simple exponen- tial smoothing is used but the smoothing coefficient is varied at each forecast by ± .05 to determine which of the three forecasts has the lowest forecast error. The resulting value of a is used for the next-period forecast. The smoothing coefficient is allowed to increase to a maximum of .95 and decrease to a minimum of .05.

Another type of adaptive smoothing is to continually adjust a on the basis of current forecast error. For example, a could be adjusted for the value of the smoothed forecasting error. If there is a large forecasting error, a will be large until the forecast comes back on track. When the error is smaller, a will also be small and a stable forecast will result. This m ethod appears to work quite well for inven- tory forecasting situations.

Table 11.5 summarizes four time-series forecasting m ethods. We have already discussed two of them, moving average and exponential smoothing. The remain- ing two are described briefly below.

A customized mathematical model can be fitted to a time series, with level, trend, and seasonal components. For example, a model can be fitted by the meth- ods of linear regression or the use of nonlinear methods. In some cases, the result- ing model may provide a more accurate forecast than exponential smoothing. However, a custom-fitted model is more expensive becau se an individual with sophisticated skills will be used to develop it, and so the trade-off between accu- racy and model cost must be made.

TABLE 11.5 Time-Series Forecasting Methods

Accuracy

Identification Time-Series Description of Medium long of Turning Relative

Methods Method Uses Short Term Term Term Point Cost

1. Moving Forecast is based on arithmetic Short- to medium-range Poor to Poor Very poor Poor Low averages average or weighted average planning for inventories, good

of a given number of past data production levels, and points. scheduling. Good for

many products.

2. Exponential Similar to moving average, with Same as moving average. Fair to Poor to Very poor Poor Low smoothing exponentially more weight very good good

placed on recent data. Well adapted to computer use and large number of items to be forecast.

3. Mathematical A linear or nonlinear model Same as moving average Very good Fair to good Very poor Poor Low to models fitted to time-series data, usually but limited, due to medium

by regression methods. Includes expense, to a few trend lines, polynomials, products. log-linear, Fourier series, etc.

4 .. Box-Jenkins Autocorrelation methods are Limited, due to expense, Very"good Fair to good Very poor Poor Medium used to identify underlying to products requiring very to excellent to high time series and to fit the accurate short-range "best" model. Requires about forecasts. 60 past data points.

Source: Reprinted by permission of the Harvard Business Review. Exhibit adapted from David M. Georgoff and Robert Murdick, "Manager's Guid e to Forecasting," Harvard Business Review, January-February 1986, pp. 110-120.

Chapter 11 Forecasting 267

Another option, the sophisticated Box-Jenkins method, has been developed for time-series forecasting. This technique has a special phase for model identifica- tion, and it permits more precise analysis of proposed models than is possible with the other methods. The Box-Jenkins method, however, requires about 60 pe- riods of past data and is too expensive to use for routine forecasting of many items. For a special forecast of sales involving a costly decision, however, the use of Box-Jenkins may be warranted.

In summar}j time-series methods are useful for short- or medium-range fore- casts when the demand pattern is expected to remain relatively stable. Time-series forecasts are often inputs to decisions concerning aggregate output planning, bud- geting, resource allocation, inventory, and scheduling. Time-series forecasts are not typically useful for decisions on facility planning or process selection because of the long time spans involved.

11.8 CAUSAL FORECASTING METHODS

/,ABLE ~1 . 6 Bgresswn

Example*

The second type of quantitative forecasting, causal forecasting methods, develop a cause-and-effect model between demand and other variables. For example, the demand for ice cream may be related to population, the average summer tempera- ture, and time. Data can be collected on these variables and an analysis conducted to determine the validity of the proposed model. One of the best-known causal methods is regression, which is usually taught in statistics courses.

For regression methods, a model must be specified before the data are collected and the analysis is conducted. The simplest case is the following single-variable linear model:

y =a+ bx where

y = estimated demand x =independent variable (hypothesized to causey) a = y intercept b =slope

Data are collected for this model, and the parameters a and b are estimated. Then estimates of demand can be made from the above equation. Of course, more com- plicated multiple regression models can also be developed.

2 3 4 5 6 7 8

Y;

3.0 3.5 4.1 4.4 5.0 5.7 6.4 7.0

39.1

2.0 2.4 2.8 3.0 3.2 3.6 3.8 4 .0

24.8

*The demand for newspap ers, y,, is expressed in thousands of copies. The population, x, is expressed in ten thousands of people.

We will illustrate linear regression forecasting with a simple example. Sup- pose we are interested in estimating the demand for newspapers on the basis of local population. The demand for news- papers over the past eight years (y;) and the corresponding population in a small town (x;) are shown in Table 11 .6. Using the available data, we first compute the values of a and b for the line. This is done by using one of many statistics packages, such as Excel, Minitab, SPSS, or SAS. The result in this case is a = -1.34 and

268 Part Four Capacity and Scheduling

b = 2.01. The best (least squares) equation for predicting demand for n ewsp a:re- is thus y = -1 .34 + 2.01x. From this equation we can see that the rate of increase newspapers is 2.01 (thousands of copies) for each 10,000-person increase in popat lation. This rate of increase, or trend, would allow us to project newspaper de-- mand in future years from population estimates, assuming that a linear equatiol continues to be a good fit with population as a predictor variable.

Other forms of causal forecasting-econometric models, input-output mode~!;~ and simulation models-are described in Table 11.7. In general, these models are more complex and more costly to develop than regression models. However, in situ:- ations in which it is necessary to model a segment of the economy in detail, an econometric or input-output model may be appropriate.

Simulation models are especially useful when a supply chain or logistics Sf9" tern is modeled for forecasting purposes. For example, suppose you want to esti- mate the demand for flat screen TVs. In this case, a simulation model can be b~ representing the distribution pipeline from the flat screen manufacturer, to the n assembler, and finally to wholesale and retail distribution chains; all imports, in- ventories, and exports from the supply chain would be included. Through the use of this model, a reasonable forecast for flat screen TVs several years into the fu ture is obtained.

One of the most important features of causal models is that they are used to predict turning points in the demand function. In contrast, time-series models can only predict future demand based on past demand; they cannot predict uptum!f and downturns in the demand level. Because of this ability to predict turiling points, causal models are usually more accurate than time-series models for me- dium- to long-range forecasts. Causal models therefore are more widely useful foe facility and process planning in operations.

11.9 SELECTING A FORECASTING METHOD

A survey of 240 U.S. firms found that about half use standard spreadsheets to cre- ate their forecasting models. Another 40 percent use specialized forecasting soft- ware, while the final 10 percent use no software. On average, commerciallj available forecasting software results in the best forecast accuracy, as measured by MAPE.3 In this section, we present a set of factors to consider for selecting from among qualitative, time-series, and causal methods. The most important factors in selecting a model are as follows:

1. User and system sophistication. How sophisticated are the managers, insid~ and outside of operations, who are expected to use the forecasting results? The forecasting method must be matched to the knowledge and sophistication of the user. Generally speaking, managers are reluctant to use results from tech- niques they do not understand.

A related factor is the status of forecasting systems currently in use. Forecast~ ing systems tend to evolve toward more mathematically sophisticated meth- ods; they do not change in one grand step. Therefore, the method chosen must not be too advanced or sophisticated for its users or too far advanced beyond the current forecasting system. Furthermore, simpler models sometimes can perform better, and so sophistication is not the ultimate goal.

3 Sanders and Manrodt (2003).

TABLE 11 .7 Causal Forecasting Methods

Causal Methods

1 . Regression

2. Econometric model

3. Input-output model

4. Simulation model

Description of Method

This method relates demand to other external or internal variables that tend to cause demand changes. The method of regression uses least squares to 'obtain a best fit between the variables.

A system of interdependent regression equations that describes some sector of economic sales or profit activity.

A method of forecasting that describes the flows from one sector of the economy to another. Predicts the inputs required to produce required outputs in another sector.

Simulation of the distribution system describing the changes in sales and flows of product over time. Reflects effects of :the distribution pipeline.

. Uses

Short- to medium-range planning for aggregate production or inventory involving a few products. Useful where strong causal relationships exist.

Forecast of sales by product classes for short- to medium-range planning.

Forecasts of company- or countrywide sales by industrial sectors.

Forecasts of companywide sales by major product g roups.

Short Term

Good to very good

Very good to excellent

Not available

Very good

Accuracy

Medium Term

Good to very good

Very good

Good to very good

Good to very good

Long Term

Poor

Good

Good to very good

Good

Identification of Turning Relative

Point Cost

Very good Medium

Excellent High

Fair Very high

Good High

Source: Reprinted by permission of the Harvard Business Review. Exhibit adap ted from David M. Georgoff and Robert Murdick, "Manager's G uide to Forecasting," Harvard Business Review, January-February 1986, pp.l1()...120.

270 Part Four Capacity aru:l Scheduling

2. Time and resources available. The selection of a forecasting method will de- pend on the time available in which to collect the data and prepare the forecast. This may involve the time of users, forecasters, and data collectors. The prepara- tion of a complicated forecast for which most of the data must be collected mav take several months and cost thousands of dollars. For routine forecasts made by computerized systems, both the cost and the amount of time required may be very modest.

3. Use or decision characteristics. The forecasting method must be related to the use or decisions required. The use, in turn, is closely related to characteristics such as accuracy required, time horizon of the forecast, and number of items to be forecast. For example, inventory, scheduling, and pricing decisions by a big box retailer require highly accurate short-range forecasts for a large number of items. Time-series methods are ideally suited to these requirements. By con- trast, decisions by an auto manufacturer involving process, facility planningJ and marketing programs are long range in nature and require less accuracy. Qualitative or causal methods tend to be more appropriate for those decisions.. In the middle time range are aggregate planning, capital-budgeting, and new- product and new-service introduction decisions, which often utilize time-serie9 or causal methods.

4. Data availability. The choice of forecasting method is often constrained bv available data. An econometric model may require data that are simply not available in the short run; therefore, another method must be selected. The Box-Jenkins time-series method requires al:fout 60 data points (five years of monthly data). The quality of the data available is also a concern. Poor data lead to poor forecasts. Data should be checked for extraneous factors or un- usual points.

5. Data pattern. The pattern in the data will affect the type of forecastirqJ method selected. If the time series is level, as we have assumed in most ot this chapter, a fairly simple method can be used. However, if the data show trends or seasonal patterns, more advanced methods will be needed. The pattern in the data will also determine whether a time-series method will suffice or whether causal models are needed. If the data pattern is unstable over time, a qualitative method may be selected. One way to detect the pat- tern is to plot the data on a graph. This should always be done as the first step in forecasting.

Recent research by Kremer, Moritz, and Siemsen (2011) in a laboratory setting may provide additional insight on the contexts in which either qualitative or quantitative methods might be preferred. They found that forecasters tend to overreact and "overadjust" to forecast errors (in their future forecasts) when de- mand has been relatively stable. Conversely, forecasters underreact to forecast errors when past demand was unstable. So, when demand is stable, m anagement should tend toward using quantitative models for forecasting, to remove human judgment that is biasing the forecast. And when demand is unstable, qualitativu methods that account for the opinions of several experts m ay be b est.

Another issue concerning the selection of for ecasting m ethods is the difference between fit and prediction. When different models are tested, it is often thoughll that the model with the best fit to historical data (least error) is also the best p re- dictive model. This is not true. For example, suppose demand observations are obtained over the last eight time periods and we want to fit the best time-series

Chapter 11 Forecasting 271

model to these data. A polynomial model of degree seven can be made to fit ex- actly through each of the past eight data points.4 However, this model is not neces- sarily the best predictor of the future.

The best predictive model is one that describes the underlying time series but is not force-fitted to the data. The correct way to fit models based on past data is to separate model fit and model prediction. First, the data set is divided into two parts. Several models based on reasonable assumptions about seasonality, trend, and cycle are then fitted to the first data set. These models are used to predict val- ues for the second data set, and the one with the lowest error on the second set is the best model. This approach utilizes fit on the first data set and prediction on the second as a basis for model selection.

11 .10 COLLABORATIVE PLANNING, FORECASTING, AND REPLENISHMENT

Collaborative planning, forecasting, and replenishment (CPFR) is a relatively new approach aimed at achieving more accurate forecasts. The basic idea is to share information between business customers and suppliers in the supply chain during the planning and forecasting process. For example, a customer may have informa- tion on future planned sales promotions or inventory adjustments that are not known to the supplier. In this case a forecast based on time-series data alone by the supplier would be inaccurate, but it could be adjusted if the customer informa- tion were made available.

Using CPFR, the customer and supplier exchange information on their respec- tive forecasted demands. When there is a discrepancy in the forecasts, a discussion ensues i:o discover the basis for the difference. After discussion, an agreed forecast is developed that becomes the basis for replenishment planning. Note, this is a forecast and not an actual order from the customer that would typically be placed at a later time. The collaborative forecast gives visibility into the replenishment planning processes beyond the usual ordering cycle.

CPFR is useful only in certain situations. It works best in B2B relationships where there are only a few customers that reflect the bulk of demand. Walmart, for example, would not use CPFR with its large numbers of retail customers, but Walmart does supply forecasted orders to its suppliers. Walmart does this by item and by store for all of its major suppliers. As a result the suppliers gain visibility into expected demand shifts, special sales promotions, and inventory adjustments that Walmart is planning. CPFR helps coordinate the Walmart supply chain. See the following Operations Leader box for another example of the use of CPFR.

The important points to remember about CPFR are:

1. All parties must be willing to share sensitive information about demand data, future sales promotions, potential orders, new products, lead times, and so forth. Assurances must be provided that competitors will not have access to this proprietary information.

2. A long-term collaborative relationship that is mutually beneficial is needed. This will require an atmosphere of trust and ongoing management attention.

3. Sufficient time and resources must be provided for CPFR to succeed. In other words, there is a cost to receive the benefits of CPFR.

272 Part Four Capacity and Scheduling

-

Operations Leader CPFR Creates Waves for West Marine - -

After 10 years of using collaborative planning, fore- casting, and replenishment (CPFR) with 200 of its ma- jor suppliers, West Marine has seen forecast accuracy rise 85 percent, and 96 percent of products are in- stock in retail stores during their peak season.

West Marine, the largest boating-supply retail chain in the United States, opened its first store in Palo Alto, Cal ifornia, in 1975. Today, they have sales of more than $690 million from over 400 stores and an active website carrying 50,000 products, from kayaks and anchors to life jackets and wetsuits . They use

CPFR to I)Ot only manage forecasting and inventory flow, but as a core business process for improving overall business performance. "Its role is similar to organizational improvements [such as) lean/Six Sigma, the SCOR Model, and sales and operations planning," writes Larry Smith, senior vice president of planning and replenishment.

During planning processes, retail stores have pri- mary responsibility for creating the demand fore- casts for each item. They use a single technology platform that is scalable across items and suppliers. Retailers base their forecasts on data such as sea- sonal forecasts, planned promotions, and future re- tail assortment changes. These forecasts are then integrated with planning at the company's distribu- tion centers and its suppliers.

West Marine gains supplier buy-in for using CPFR by working closely with them to accommo- date their materials planning schedules. Suppliers will know about specia ~ promotions well in advance so that lead times (often international) can be man- aged. To make its commitment to CPFR and its sup- pliers clear, West Marine guarantees it will purchase its forecasts.

Source: Larry Smith. "West Marine: A CPFR Success Story," Supply Chain Management Review, March 1, 2006.

Whirlpool uses CPFR to forecast sales of appliances by its key trading p art-

Whirlpool uses CPFR to reduce forecast errors for its appliances.

ners (e.g., Sears). Traditionally, Whirlpool and its trading partners each

~~~ · · ~-.i ' :· --- '

independently created a sales fore- cast for each market. Using CPFR, they share their forecasts electroni- cally and then work to reduce differ- ences. Before CPFR, the av erage forecast error was 100 percent of d e- mand due to the small quantity of appliances sold in the typical store. After the use of CPFR, the forecast err or was reduced to 45 percent of

demand. To unde rstand the enormity of this change, each p ercentage point reduction in forecast error reduced Whirlpool' s inventory by several million dollars.5

5 R. E. Slone (2004).

Chapter 11 Forecasting 273

1.11 KEY POINTS AND TERMS

ey Terms

Demand forecasts are crucial inputs to planning decisions within operations and other parts of business. In this chapter, we have highlighted several important uses and methods of forecasting. Some of the chapter ' s main points are the following:

• Different decisions require different forecasting methods, including the follow- ing decisions in operations: process design, capacity planning, aggregate plan- ning, scheduling, and inventory management. Some of the decisions outside of operations that require forecasts are long-range marketing programs, pricing, new-product and new-service introduction, cost estimating, and capital bud- geting. The available methods may be classified as qualitative, time-series, and causal methods.

• Four of the most important qualitative methods are Delphi, market surveys, life- cycle analogy, and informed judgment. These methods are most useful when his- torical data are not available or are not reliable in predicting the future. Qualitative methods are used primarily for long- or medium-range forecasting involving process design, facilities planning, and marketing programs.

• Time-series forecasting is used to decompose demand data into their underlying components and thereby to project the historical pattern forward in time. The primary uses are short- to medium-term forecasting for inventory, scheduling, pricing, and costing decisions. Some of the best-known time-series techniques are the moving average, exponential smoothing, mathematical models, and the Box-Jenkins method.

• Causal forecasting methods include regression, econometric models, input- output models, and simulation models. These methods are used in an attempt to establish a cause-and-effect relationship between demand and other variables. Causal methods can help in predicting turning points in time-series data and are therefore most useful for medium- to long-range forecasting.

• Two measures of accuracy in forecasting are bias and deviation. Both should be monitored routinely to control the accuracy of the forecasts obtained. For fore- casting applications, tracking signal and MAD are two methods used to deter- mine if bias and deviation, respectively, are well controlled.

• A forecasting method should be selected on the basis of five factors : user and system sophistication, time and resources available, use or decision characteris- tics, data availability, and data pattern.

• CPFR is a method used to share and improve forecasts between customers and suppliers along the supply chain and thereby reduce forecasting errors.

Qualitative forecasting methods 254

Quantitative forecasting methods 254

Time-series methods 257 Level 257 Trend 257 Seasonality 257 Cycle 257 Random error 257

Moving-av erage method 258

Forecast error 259 Weighted moving

average 260 Exponential

smoothing 260 Simple exponential

smoothing 261 Bias 262

Absolute deviation 262

Forecastaccuracy 263 Adaptive exponential

smoothing 265 Causal forecasting

methods 267 Fit 270 Prediction 270 CPFR 271