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Forecasting

 

Contents

  • Forecasting is a prelude to planning. Before making plans, an estimate must be made of what conditions will exist over some future period. How estimates are made, and with what accuracy, is another matter, but little can be done without some form of estimation.

  • Why forecast? There are many circumstances and reasons, but forecasting is inevitable in developing plans to satisfy future demand. Most firms cannot wait until orders are actually received before they start to plan what to produce. Customers usually demand delivery in reasonable time, and manufacturers must anticipate future demand for products or services and plan to provide the capacity and resources to meet that demand. Firms that make standard products need to have saleable goods immediately available or at least to have materials and subassemblies available to shorten the delivery time. Firms that make to order cannot begin making a product before a customer places an order but must have the resources of labor and equipment available to meet demand.

  • Many factors influence the demand for a firm’s products and services. Although it is not possible to identify all of them, or their effect on demand, it is helpful to consider some major factors:

    • General business and economic conditions.

    • Competitive factors.

    • Market trends such as changing demand.

    • The firm’s own plans for advertising, promotion, pricing, and product changes.

  • The prime purpose of an organization is to serve the customer. Marketing focuses on meeting customer needs, but operations, through materials management, must provide the resources. The coordination of plans by these two parties is demand management.

a. Demand management

  • Demand management is the function of recognizing and managing all demands for products. It occurs in the short, medium, and long term. in the long term, demand projections are needed for strategic business planning of such things as facilities. In the medium term, the purpose of demand management is to project aggregate demand for production planning. In the short run, demand management is needed for items and is associated with master production scheduling. We are most concerned with the latter.

  • If material and capacity resources are to be planned effectively, all sources of demand must be identified. These include domestic and foreign customers, other plants in the same corporation, branch warehouses, service parts and requirements, promotions, distribution inventory, and consigned inventory in customers’ locations.
    Demand management includes four major activities:

    • Forecasting.

    • Order processing.

    • Making delivery promises. The concept of available-to-promise was discussed in Chapter 3.

    • Interfacing between manufacturing planning and control and the marketplace. Figure 8.1 shows this relationship graphically.

b. Order processing.

  • Order processing occurs when a customer’s order is received. The product may be delivered from finished goods inventory or it may be made or assembled to order. if goods are sold from inventory, a sales order is produced authorizing the goods to be shipped from inventory. If the product is made or assembled to

  • order, the sales department must write up a sales order specifying the product. This may be relatively simple if the product is assembled from standard components but can be a lengthy, complex process if the product requires extensive engineering. A copy of the sales order stating the terms and conditions of acceptance of the order is sent to the customer. Another copy, sent to the master planner, is authorization to go ahead and plan for manufacture. The master planner must know what to produce, how much, and when to deliver. The sales order must be written in language that makes this information clear.

3. Demand Forecasting

  • Forecasts depend upon what is to be done. They must be made for the strategic business plan, the production plan, and the master production schedule. As discussed in Chapter 2, the purpose, planning horizons, and level of detail vary for each.

  • The strategic business plan is concerned with overall markets and the direction of the economy over the next two to ten years or more. Its purpose is to provide time to plan for those things that take long to change. For production, the strategic business plan should provide sufficient time for resource planning: plant expansion, capital equipment purchase, and anything requiring a long lead time to purchase. The level of detail is not high, and usually forecasts are in sales units, sales dollars, or capacity. Forecasts and planning will probably be reviewed quarterly or yearly.

  • Production planning is concerned with manufacturing activity for the next one to three years. For manufacturing, it means forecasting those items needed for production planning, such as budgets, labor planning, long lead time, procurement items, and overall inventory levels. Forecasts are made for groups or families of products rather than specific end items. Forecasts and plans will probably be reviewed monthly.

  • Master production scheduling is concerned with production activity from the present to a few months ahead. Forecasts are made for individual items, as found on a master production schedule, individual item inventory levels, raw materials and component parts, labor planning, and so forth. Forecasts and plans will probably be reviewed weekly.

  • In this chapter, the term “demand” is used rather than “sales.” The difference is that sales implies what is actually sold whereas demand shows the need for the item. Sometimes demand cannot be satisfied, and sales will be less than demand.

  • Before discussing forecasting principles and techniques, it is best to look at some characteristics of demand that influence the forecast and the particular techniques used.

a. Demand Patterns

  • If historical data for demand are plotted against a time scale, they will show any shapes or consistent patterns that exist. A pattern is the general shape of a time series.

  • Although some individual data points will not fall exactly on the pattern, they tend to cluster around it.

  • Figure 8.2 shows a hypothetical historical demand pattern. The pattern shows that actual demand varies from period to period. There are four reasons for this:
    trend, seasonality, random variation, and cycle.

Trend.

  • Figure 8.2 shows that demand is increasing in a steady pattern of demand from year to year. This graph illustrates a linear trend, but there are different shapes, such as geometric or exponential. The trend can be level, having no change from period to period, or it can rise or fall.

Seasonality.

  • The demand pattern in Figure 8.2 shows each year’s demand fluctuating depending on the time of year. This fluctuation may be the result of the weather, holiday seasons, or particular events that take place on a seasonal basis. Seasonality is usually thought of as occurring on a yearly basis, but it can also occur on a weekly or even daily basis. A restaurant’s demand varies with the hour of the day, and supermarket sales vary with the day of the week.

Random variation.

  • Random variation occurs where many factors affect demand during specific periods and occur on a random basis. The variation may be small, with actual demand falling close to the pattern, or it may be large, with the points widely scattered. The pattern of variation can usually be measured, and this will be discussed in the section on tracking the forecast.

 

Cycle.

  • Over a span of several years and even decades, wavelike increases and decreases in the economy influence demand. However, forecasting of cycles is a job for economists and is beyond the scope of this text.

b. Stable versus Dynamic

  • The shapes of the demand patterns for some products or services change over time whereas others do not. Those that retain the same general shape are called stable and those that do not are called dynamic. Dynamic changes can affect the trend, seasonality, or randomness of the actual demand. The more stable the demand, the easier it is to forecast. Figure 8.3 shows a graphical representation of stable and dynamic demand. Notice the average demand is the same for both stable and dynamic patterns. It is usually the average demand that is forecast.

c. Dependent versus Independent Demand

  • Chapter 4 discussed dependent and independent demand. It was said that demand for a product or service is independent when it is not related to the demand for any other product or service. Dependent demand for a product or service occurs where the demand for the item is derived from that of a second item. Requirements for dependent demand items need not be forecast but are calculated from that of the independent demand item.

  • Only independent demand items need be forecast. These are usually end items or finished goods but should also include service parts and items supplied to other plants in the same company (inter-company transfers).

  • Forecasts have four major characteristics or principles. An understanding of these will allow us to make more effective use of forecasts. They are simple and, to some extent, common sense.

  1. Forecasts are usually wrong. Forecasts attempt to look into the unknown future and, except by sheer luck, will be wrong to some degree. Errors are inevitable and must be expected.

  2. Every forecast should include an estimate of error. Since forecasts are expected to be wrong, the real question is, “By how much?” Every forecast should include an estimate of error often expressed as a percentage (plus and minus) of the forecast or as a range between maximum and minimum values. Estimates of this error can be made statistically by studying the variability of demand about the average demand.

  3. Forecasts are more accurate for families or groups. The behavior of individual items in a group is random even when the group has very stable characteristics. For example, the marks for individual students in a class are more difficult to forecast accurately than the class average. High marks average out with low marks. This means that forecasts are more accurate for large groups of items than for individual items in a group.
    For production planning, families or groups are based on the similarity of process and equipment used. For example, a firm forecasting the demand for knit socks as a product group might forecast men’s socks as one group and women’s as another since the markets are different. However, production of men’s and women’s ankle socks will be done on the same machines and knee socks on another. For production planning, the forecast should be for (a) men’s and women’s ankle socks and (b) men’s and women’s knee socks.

  4. Forecasts are more accurate for nearer time periods. The near future holds less uncertainty than the far future. Most people are more confident in forecasting what they will be doing over the next week than a year from now. As someone once said, tomorrow is expected to be pretty much like today.
    In the same way, demand for the near term is easier for a company to forecast than for a time in the distant future. This is extremely important for long lead-time items and especially so if their demand is dynamic. Anything that can be done to reduce lead time will improve forecast accuracy.

6. Collection And Preparation Of Data

  • Forecasts are usually based on historical data manipulated in some way using either judgment or a statistical technique. Thus, the forecast is only as good as the data on which it is based. To get good data, three principles of data collection are important.

    1. Record data in the same terms as needed for the forecast. This is a problem in determining the purpose of the forecast and what is to be forecast. There are three dimensions to this:

      1. If the purpose is to forecast demand on production, data based on demand, not shipments, are needed. Shipments show when goods were shipped and not necessarily when the customer wanted them. Thus shipments do not necessarily give a true indication of demand.

      2. The forecast period, in weeks, months, or quarters, should be the same as the schedule period. If schedules are weekly, the forecast should be for the same time interval.

      3. The items forecast should be the same as those controlled by manufacturing. For example, if there are a variety of options that can be supplied with a particular product, the demand for the product and for each option should be forecast.

  • Suppose a firm makes a bicycle that comes in three frame sizes, three possible wheel sizes, a 3-, 5-. or 10-speed gear changer, and with or without deluxe trim. In all, there are 54 (3 x 3 x 3 x 2) individual end items sold. If each were forecast, there would be 54 forecasts to make. A better approach is to forecast (a) total demand and (b) the percentage of the total that requires each frame size, wheel size, and so on. That way there need be only 12 forecasts (three frames, three wheels, five gears, and the bike itself).

  • In this example, the lead time to make the components would be relatively long in comparison to the lead time to assemble a bike. Manufacturing can make the components according to component forecast and can then assemble bikes according to customer orders. This would be ideal for situations where final assembly schedules are used.

    1. Record the circumstances relating to the data. Demand is influenced by particular events, and these should be recorded along with the demand data. For instance, artificial bumps in demand can be caused by sales promotions, price changes, changes in the weather, or a strike at a competitor’s factory. It is vital that these factors be related to the demand history so they may be included or removed for future conditions.

    2. Record the demand separately for different customer groups. Many firms distribute their goods through different channels of distribution, each having its own demand characteristics. For example, a firm may sell to a number of wholesalers that order relatively small quantities regularly and also sell to a major retailer that buys a large lot twice a year. Forecasts of average demand would be meaningless, and each set of demands should be forecast separately.

  • There are many forecasting methods, but they can usually be classified into three categories: qualitative, extrinsic, and intrinsic.

a. Qualitative Techniques

  • Qualitative techniques are projections based on judgment, intuition, and informed opinions. By their nature, they are subjective. Such techniques are used to forecast genera! business trends and the potential demand for large families of products over an extended period of time. As such, they are used mainly by senior management. Production and inventory forecasting is usually concerned with the demand for particular end items, and qualitative techniques are seldom appropriate.

  • When attempting to forecast the demand for a new product, there is no history on which to base a forecast. In these cases, the techniques of market research and historical analogy might be used. Market research is a systematic, formal, and conscious procedure for testing to determine customer opinion or intention. Historical analogy is based on a comparative analysis of the introduction and growth of similar products in the hope that the new product behaves in a similar fashion. Another method is to test-market a product.

  • There are several other methods of qualitative forecasting. One, called the Delphi method, uses a panel of experts to give their opinion on what is likely to happen.

b. Extrinsic Techniques

  • Extrinsic forecasting techniques are projections based on external (extrinsic) indicators which relate to the demand for a company’s products. Examples of such data would be housing starts, birth rates, and disposable income. The theory is that the demand for a product group is directly proportional, or correlates, to activity in another field. Examples of correlation are:

    • Sales of bricks are proportional to housing starts.

    • Sales of automobile tires are proportional to gasoline consumption.

  • Housing starts and gasoline consumption are called economic indicators. They describe economic conditions prevailing during a given time period. Some commonly used economic indicators are construction contract awards, automobile production, farm income, steel production, and gross national income. Data of this kind are compiled and published by various government departments, financial papers and magazines, trade associations, and banks.

  • The problem is to find an indicator that correlates with demand and one that preferably leads demand, that is, one that occurs before the demand does. For example, the number of construction contracts awarded in one period may determine the building material sold in the next period. When it is not possible to find a leading indicator, it may be possible to use a nonleading indicator for which the government or an organization forecasts. In a sense, it is basing a forecast on a forecast.

  • Extrinsic forecasting is most useful in forecasting the total demand for a firm’s products or the demand for families of products. As such, it is used most often in business and production planning rather than the forecasting of individual end items.

c. Intrinsic Techniques

  • Intrinsic forecasting techniques use historical data to forecast. These data are usually recorded in the company and are readily available. Intrinsic forecasting techniques are based on the assumption that what happened in the past will happen in the future. This assumption has been likened to driving a car by looking out the rear-view mirror. While there is some obvious truth to this, it is also true that lacking any other “crystal ball,” the best guide to the future is what has happened in the past.

  • Since intrinsic techniques are so important, the next section will discuss some of the more important techniques. They are often used as input to master production scheduling where end-item forecasts are needed for the planning horizon of the plan.

  • Assume that the monthly demand for a particular item over the past year is as shown in Figure 8.4.
    Suppose it is the end of December, and we want to forecast demand for January of the coming year. Several rules can be used:

    • Demand this month will be the same as last month. January demand would be forecast at 84, the same as December. This may appear too simple, but if there is little change in demand month to month, it probably will be quite usable.

    • Demand this month will be the same as demand the same month last year. Forecast demand would be 92, the same as January last year. This rule is adequate if demand is seasonal and there is little up or down trend.

  • Rules such as these, based on a single month or past period, are of limited use when there is much random fluctuation in demand. Usually methods that average out history are better because they dampen out some effects of random variation.

  • As an example, the average of last year’s demand can be used as an estimate for January demand. Such a simple average would not be responsive to trends or changes in level of demand. A better method would be to use a moving average.

  • Average demand. This raises the question of what to forecast. As discussed earlier, demand can fluctuate because of random variation. It is best to forecast the average demand rather than second-guess what the effect of random fluctuation will be. The second principle of forecasting discussed earlier said that a forecast should include an estimate of error. As we will see later, this range can be estimated. Thus, a forecast of average demand should be made, and the estimate of error applied to it.

a. Moving Averages

  • One simple way to forecast is to take the average demand for, say, the last three or six periods and use that figure as the forecast for the next period. At the end of the next

                                     January               92              July                     84

                                     February              83              August                81

                                     March                 66              September            75

                                      April                  74              October                 63 

                                      May                  75              November               91

                                       June                 84              December              84

 

  • period, the first-period demand is dropped and the latest-period demand added to determine a new average to be used as a forecast. This forecast would always be based on the average of the actual demand over the specified period.

  • For example, suppose it was decided to use a three-month moving average on the data shown in Figure 8.4. Our forecast for January, based on the demand in October, November, and December, would be:

                                         63 91 + 84               

                                                               .  = 79

                                                  3

  • Now suppose that January demand turned out to be 90 instead of 79. The forecast for February would be calculated as:

                                          91 + 84 + 90

                                                                  = 88

                                                   3

b. Example Problem

  • Demand over the past three months has been 120, 135, and 114 units. Using a three-month moving average, calculate the forecast for the fourth month.

Answer

                                          120 + 135 + 114        369

Forecast for month 4 =                                   =           = 123

                                                       3                       3

  • Actual demand for the fourth month turned out to be 129. Calculate the forecast for the fifth month.

                                               135+114+129

Forecast for month 5 =                                             = 126

                                                        3

  • In the previous discussion, the forecast for January was 79, and the forecast for February was 88. The forecast has risen, reflecting the higher January value and the dropping of the low October value. If a longer period, such as six months, is used, the forecast does not react as quickly. The fewer months included in the moving average, the more weight is given to the latest information, and the faster the forecast reacts to trends. However, the forecast will always lag behind a trend. For example, consider the following demand history for the past five periods:

Period

Demand

1

1000

2

2000

3

3000

4

4000

5

5000

  • There is a rising trend to demand. If a five-period moving average is used, the forecast for period 6 is (1000 + 2000 + 3000 + 4000 + 5000) 5 = 3000. It does not look
    very accurate since the forecast is lagging actual demand by a large amount. However,
    if a three-month moving average is used, the forecast is (3000 + 4000 + 5000) ± 3
    4000. Not perfect, but somewhat better. The point is that a moving average always lags
    a trend, and the more periods included in the average, the greater the lag will be.

  • On the other hand, if there is no trend but actual demand fluctuates considerably due to random variation, a moving average based on a few periods reacts to the fluctuation rather than forecasts the average. Consider the following demand history:

Period

Demand

1

2000

2

5000

3

3000

4

1000

5

4000

  • The demand has no trend and is random. If a five-month moving average is used, the forecast for the next month is 3000. This reflects all the values. If a two-month average is taken, the forecasts for the third, fourth, fifth, and sixth months are:

Forecast for third month = (2000 + 5000) ÷ 2 = 3500

Forecast for fourth month = (5000 + 3000) ÷ 2 = 4000

Forecast for fifth month = (3000 + 1000) ÷ 2 = 2000

Forecast for sixth month = (1000 + 4000) ÷ 2 2500

  • With a two-month moving average the forecast reacts very quickly to the latest demand and thus is not stable.

  • Moving averages are best used for forecasting products with stable demand where there is little trend or seasonality. Moving averages are also useful to filter out random fluctuations. This has some common sense since periods of high demand are often followed by periods of low demand.

  • One drawback to using moving averages is the need to retain several periods of history for each item to be forecast. This will require a great deal of computer storage or clerical effort. Also, the calculations are cumbersome. A common forecasting technique, called exponential smoothing, gives the same results as a moving average but without the need to retain as much data and with easier calculations.

c. Exponential Smoothing

  • It is not necessary to keep months of history to get a moving average because the previously calculated forecast has already allowed for this history. Therefore, the forecast can be based on the old calculated forecast and the new data.

  • Using the data in Figure 8.4, suppose an average of the demand of the last six months (80 units) is used to forecast January demand. If at the end of January, actual demand is 90 units, we must drop July’s demand and pick up January’s demand to determine the new forecast. However, if an average of the old forecast (80) and the actual demand for January (90) is taken, the new forecast for February is 85 units. This formula puts as much weight on the most recent month as on the old forecast (all previous months). If this does not seem suitable, less weight could be put on the latest actual demand and more weight on the old forecast. Perhaps putting only 10% of the weight on the latest month’s demand and 90% of the weight on the old forecast would be better. In that case,

February forecast = 0.1(90) + 0.9(80) = 81

  • Notice that this forecast did not rise as much as our previous calculation in which the old forecast and the latest actual demand were given the same weight. One advantage to exponential smoothing is that the new data can be given any weight wanted.
    The weight given to latest actual demand is called a smoothing constant and is represented by the Greek letter alpha (a). It is always expressed as a decimal from 0 to 1.0.

  • In general, the formula for calculating the new forecast is:

New forecast = (a) latest demand) + (1 — a) previous forecast)

d. Example Problem

  • The old forecast for May was 220, and the actual demand for May was 190. If alpha (a) is 0.15, calculate the forecast for June. If June demand turns out to be 218, calculate the forecast for July.

Answer

June forecast = (0.15)(190) + (1 — 0.15)(220) = 215.5

July forecast = (0.15)(218) + (0.85)(215.5) = 215.9

  • Exponential smoothing provides a routine method for regularly updating item forecasts. It works quite well when dealing with stable items. Generally, it has been found satisfactory for short-range forecasting. It is not satisfactory where the demand is low or intermittent.
     

  • Exponential smoothing will detect trends, although the forecast will lag actual demand if a definite trend exists. Figure 8.5 shows a graph of the exponentially smoothed forecast lagging the actual demand where a positive trend exists. Notice the forecast with the larger a follows actual demand more closely.

  • If a trend exists, it is possible to use a slightly more complex formula called double exponential smoothing. This technique uses the same principles but notes whether each successive value of the forecast is moving up or down on a trend line. Double exponential smoothing is beyond the scope of this text.

  • A problem exists in selecting the “best” alpha factor. If a low factor such as 0.1 is used, the old forecast will be heavily weighted, and changing trends will not be picked up as quickly as might be desired. If a larger factor such as 0.4 is used, the forecast will react sharply to changes in demand and will be erratic if there is a sizable random fluctuation. A good way to get the best alpha factor is to use computer simulation. Using past actual demand, forecasts are made with different alpha factors to see which one best suits the historical demand pattern for particular products.

9. Seasonality

  • Many products have a seasonal or periodic demand pattern: skis, lawnmowers, bathing suits, and Christmas tree lights are examples. Less obvious are products whose demand varies by the time of day, week, or month. Examples of these might be electric power usage during the day or grocery shopping during the week. Power usage peaks between 4 and 7 p.m., and supermarkets are most busy toward the end of the week or before certain holidays.

a. Seasonal Index

  • A useful indication of the degree of seasonal variation for a product is the seasonal index. This index is an estimate of how much the demand during the season will be above or below the average demand for the product. For example, swimsuit demand might average 100 per month, but in July the average is 175 and in September, 35. The index for July demand would be 1.75 and for September, 0.35.

  • The formula for the seasonal index is:

                                                              Period average demand

                       Seasonal index =                                                            .

                                                        Average demand for all periods

  • The period can be daily, weekly, monthly, or quarterly depending on the basis for the seasonality of demand.

  • The average demand for all periods is a value that averages out seasonality. This is called the deseasonalized demand. The previous equation can be rewritten as:

                                                         period average demand

                       Seasonal index =                                                .

                                                         deseasonalized demand

b. Example Problem

  • A product that is seasonally based on quarterly demand and the demand for the past three years is shown in Figure 8.6. There is no trend, but there is definite seasonality. Average quarterly demand is 100 units. Figure 8.6 also shows a graph of actual seasonal demand and average quarterly demand. The average demand shown is the historical average demand for all periods. Remember we forecast average demand, not seasonal demand.

Answer

The seasonal indices can now be calculated as follows:

                                                              128

                             Seasonal index =               = 1.28 (quarter 1)

                                                               100

                                                               102

                                                         =               = 1.2 (quarter 2)

                                                                 75

                                                                 75

                                                          =               = 0.75 (quarter 3)

                                                                 100

                                                                   95

                                                           =               = 0.95 (quarter 4)

                                                                  100                    

                             Total of seasonal indices =     4.00

  • Note that the total of all the seasonal indices equals the number of periods. This is a good way to check whether the calculations are correct.

Year

Quarter

 

1

2

3

4

Total

1

122

108

81

90

401

2

130

100

73

96

399

3

132

98

71

99

400

Average

128

102

75

95

400

 

c. Seasonal Forecasts

  • The equation for developing seasonal indices is also used to forecast seasonal demand. If a company forecasts average demand for all periods, the seasonal indices can be used to calculate the seasonal forecasts. Changing the equation around we get:

Seasonal demand = (seasonal index) (deseasonalized demand)

d. Example Problem

  • The company in the previous problem forecasts an annual demand next year of 420 units. Calculate the forecast for quarterly sales.

Answer

                                                                     420

Forecast average quarterly demand =                = 105 units

                                                                        4

Expected quarter demand = (seasonal index) (forecast quarterly demand)

Expected first-quarter demand = 1.28 x 105 = 134.4 units

Expected second-quarter demand = 1.02 x 105 = 107.1 units

Expected third-quarter demand = 0.75 x 105 = 78.75 units

Expected fourth-quarter demand = 0.95 x 105 = 99.75 units

                                                                                                 

            Total forecast demand                             = 420 units

 

e. Deseasonalized Demand

  • Forecasts do not consider random variation. They are made for average demand, and seasonal demand is calculated from the average using seasonal indices. Figure 8.7 shows both actual demand and forecast average demand. The forecast average demand is also the deseasonalized demand. Historical data are of actual seasonal demand, and they must be deseasonalized before they can be used to develop a forecast of average demand.

  • Also, if comparisons are made between sales in different periods, they are meaningless unless deseasonalized data are used. For example, a company selling tennis rackets finds demand is usually largest in the summer. However, some people play indoor tennis, so there is demand in the winter months as well. If demand in January was 5200 units and in June was 24,000 units, how could January demand be compared to June demand to see which was the better demand month? If there is seasonality, comparison of actual demand would be meaningless. Deseasonalized data are needed to make a comparison.

  • The equation to calculate deseasonalized demand is derived from the previous seasonal equation and is as follows:

                                                           actual seasonal demand

           Deseasonalized demand =                                              .

                                                              seasonal index

f. Example Problem

  • A company selling tennis rackets has a January demand of 5200 units and a July demand of 24,000 units. If the seasonal indices for January were 0.5 and for June were 2.5, calculate the deseasonalized January and July demand. How do the two months compare?

Answer

Deseasonalized January demand = 5200 ± 0.5 10,400 units

Deseasonalized June demand = 24,000 2.5 = 9600 units

  • June and January demand can now be compared. On a deseasonalized basis, January demand is greater than June demand.

  • Deseasonalized data must be used for forecasting. Forecasts are made for average demand, and the forecast for seasonal demand is calculated from the average demand using the appropriate season index.
    The rules for forecasting with seasonality are:

    • Only use deseasonalized data to forecast.

    • Forecast deseasonalized demand, not seasonal demand.

    • Calculate the seasonal forecast by applying the seasonal index to the base forecast.

g. Example Problem

  • A company uses exponential smoothing to forecast demand for its products. For April, the deseasonalized forecast was 1000, and the actual seasonal demand was 1250 units. The seasonal index for April is 1.2 and for May is 0.7. If cx is 0.1, calculate:

    1. The deseasonalized actual demand for April.

    2. The deseasonalized May forecast.

    3. The seasonal forecast for May.

Answer

                                                                               1250

a. Deseasonalized actual demand for April =                =1042

                                                                                  1.2

b. Deseasonalized May forecast = cx (latest actual) + 1 cx )

                                                                (previous forecast)

                                                         =      0.1(1042) + 0.9(1000) = 1004

c. Seasonalized May forecast      = (seasonal index)

                                                            (deseasonalized forecast)

                                                         = 0.7(1004) = 703

 

 

  • As noted in the discussion on the principles of forecasting, forecasts are usually wrong. There are several reasons for this, some of which are related to human involvement and others to the behavior of the economy. If there were a method of determining how good a forecast is, forecasting methods could be improved and better estimates could be made accounting for the error. There is no point in continuing with a plan based on poor forecast data. We need to track the forecast. Tracking the forecast is the process of comparing actual demand with the forecast.

a. Forecast Error

  • Forecast error is the difference between actual demand and forecast demand. Error can occur in two ways: bias and random variation.

  • Bias. Cumulative actual demand may not be the same as forecast. Consider the data in Figure 8.8. Actual demand varies from forecast, and over the six-month period, cumulative demand is 120 units greater than expected.

  • Bias exists when the cumulative actual demand varies from the cumulative forecast. This means the forecast average demand has been wrong. In the example in Figure 8.8, the forecast average demand was 100, but the actual average demand was 720 ± 6 = 120 units. Figure 8.9 shows a graph of cumulative forecast and actual demand.

  • Bias is a systematic error in which the actual demand is consistently above or below the forecast demand. When bias exists, the forecast should be changed to improve its accuracy.

Month

Forecast Actual

 

Monthly

Cumulative

Monthly

Cumulative

1

100

100

110

110

2

100

200

125

235

3

100

300

120

355

4

100

400

125

480

5

100

500

130

610

6

100

600

110

720

Total

600

600

720

720

 

  • The purpose of tracking the forecast is to be able to react to forecast error by planning around it or by reducing it. When an unacceptably large error or bias is observed, it should be investigated to determine its cause.

  • Often there are exceptional one-time reasons for error. Examples are machine breakdown, customer shutdown, large one-time orders, and sales promotions. These reasons relate to the discussion on collection and preparation of data and the need to record the circumstances relating to the data. On these occasions, the demand history must be adjusted to consider the exceptional circumstances.

  • Errors can also occur because of timing. For example, an early or late winter will affect the timing of demand for snow shovels although the cumulative demand will be the same.

  • Tracking cumulative demand will confirm timing errors or exceptional one-time events. The following example illustrates this. Note that in April the cumulative demand is back in a normal range.

Month

Forecast

Actual

Cumulative Forecast

Cumulative Actual

February

100

110

200

205

March*

100

155

300

360

April

100

45

400

405

May

100

90

500

495

* Customer foresaw a possible strike and stockpiled.

Month

Forecast

Actual

Variation (error)

1

100

105

5

2

100

94

-6

3

100

98

-2

4

100

104

4

5

100

103

3

6

100

96

-4

Total

600

600

0

Random variation.

  • In a given period, actual demand will vary about the average demand. The variability will depend upon the demand pattern of the product. Some products will have a stable demand, and the variation will not be large. Others will be unstable and will have a large variation.

  • Consider the data in Figure 8.10, showing forecast and actual demand. Notice there is much random variation, but the average error is zero. This shows that the av­erage forecast was correct and there was no bias. The data are plotted in Figure 8.11.

b. Mean Absolute Deviation

  • Forecast error must be measured before it can be used to revise the forecast or to help in planning. There are several ways to measure error, but one commonly used is mean absolute deviation (MAD).

  • Consider the data on variability in Figure 8.10. Although the total error (variation) is zero, there is still considerable variation each month. Total error would be useless to measure the variation. One way to measure the variability is to calculate the total error ignoring the plus and minus signs and take the average. This is called mean absolute deviation:

    • mean implies an average,

    • absolute means without reference to plus and minus,

    • deviation refers to the error:

                                                  sum of absolute deviations

                                   MAD =                                                   .

                                                    number of observations

 

c. Example Problem

  • Given the data shown in Figure 8.10, calculate the mean absolute deviation.

Answer

                    Sum of absolute deviations = 5 + 6 + 2 + 4 + 3 + 4 = 24

                                                24

                                      MAD=                       =4

                                                           6

d. Normal distribution

  • The mean absolute deviation measures the difference (error) between actual demand and forecast. Usually, actual demand is close to the forecast but sometimes is not. A graph of the number of times (frequency) actual demand is of a particular value produces a bell-shaped curve. This distribution is called a normal distribution and is shown in Figure 8.12. Chapter 11 gives a more detailed discussion of normal distributions and their characteristics.

  • There are two important characteristics to normal curves: the central tendency, or average, and the dispersion, or spread, of the distribution. In Figure 8.12, the central tendency is the forecast. The dispersion, the fatness or thinness of the normal curve, is measured by the standard deviation. The greater the dispersion, the larger

  • the standard deviation. The mean absolute deviation is an approximation of the standard deviation and is used because it is easy to calculate and apply.

  • From statistics we know that the error will be within:

± 1 MAD of the average about 60% of the time

±2 MAD of the average about 90% of the time

±3 MAD of the average about 98% of the time.

e. Uses of mean absolute deviation.

  • Mean absolute deviation has several uses. Some of the most important follow.

  • Tracking signal. Bias exists when cumulative actual demand varies from forecast. The problem is in guessing whether the variance is due to random variation or bias. If the variation is due to random variation, the error will correct itself, and nothing should be done to adjust the forecast. However, if the error is due to bias, the forecast should be corrected. Using the mean absolute deviation, we can make some judgment about the reasonableness of the error. Under normal circumstances, the actual period demand will be within ± 3 MAD of the average 98% of the time. If actual period demand varies from the forecast by more than 3 MAD, we can be about 98% sure that the forecast is in error.

  • A tracking signal can be used to monitor the quality of the forecast. There are several procedures used, but one of the simpler is based on a comparison of the cumulative sum of the forecast errors to the mean absolute deviation. Following is the equation:

                                                  algebraic sum of forecast errors

                  Tracking signal =                                                               .

                                                                        MAD

f. Example Problem

  • The forecast is 100 units a week. The actual demand for the past six weeks has been 105, 110, 103, 105, 107, and 115. If MAD is 7.5, calculate the sum of the forecast error and the tracking signal.

Answer

Sum of forecast error =5 + 10 + 3 + 5 + 7+ 15 = 45

Tracking signal = 45 ÷7.5 = 6

g. Example Problem

  • A company uses a trigger of ±4 to decide whether a forecast should be reviewed. Given the following history, determine in which period the forecast should be reviewed. MAD for the item is 2.

Period

Forecast

Actual

Deviation

Cumulative

Deviation

Tracking

Signal

 

     

5

2.5

1

100

96

 

 

 

2

100

98

 

 

 

3

100

104

 

 

 

4

100

110

 

 

 

Answer

Period

 

Forecast

Actual

Deviation

Cumulative

Deviation

Tracking

Signal

 

     

5

2.5

1

100

96

-4

1

0.5

2

100

98

-2

-1

-0.5

3

100

104

4

3

1.5

4

100

110

10

13

6.5

The forecast should be reviewed in period 4.

  • Contingency planning. Suppose a forecast is made that demand for door slammers will be 100 units and that capacity for making them is 110 units. Mean absolute deviation of actual demand about the forecast historically has been calculated at 10 units. This means there is a 60% chance that actual demand will be between 90 and 110 units and a 40% chance that they will not. With this information, manufacturing management might he able to devise a contingency plan to cope with the possible extra demand.

  • Safely stock The data can be used as a basis for setting safety stock. This will be dis¬cussed in detail in Chapter 11.

h. P/D Ratio

  • Because of the inherent error in forecasts, companies who rely on them can run into a variety of problems. For example, the wrong material may be bought and perhaps processed into the wrong goods. A more reliable way of producing what is really needed is the use of the P/D ratio.

  • P,” or production lead time, is the stacked lead time for a product. It includes time for purchasing of raw materials to arrive, manufacturing, assembly, delivery, and sometimes the design of the product. Figure 1.1. on page 4 shows various times in different types of industries and is reproduced here as Figure 8.13

  • "D," or demand lead time, is the customer’s lead time. it is the time from when a customer places an order until the goods are delivered, it can be very short, as in a make-to-stock environment, or very long, as an engineer-to-order company.
    The traditional way to guard against inherent error in forecasting is to include safety stock in inventory. There is an added expense to the extra inventory carried “just in case.” One other way is to make more accurate predictions. There are five ways to move in this direction.

    1. Reduce P time. The longer the P time, the more chance there is for error. Ideally, P will be less than D.

    2. Force a match between P and D. Moving in this direction can be done in two ways:
      a. Make the customer’s D time equal to your P time. This is common with custom products when the manufacturer makes the product according to the customer’s specification.

    3. Sell what you forecast. This will happen while you control the market. One good example is the automobile market. It is common to offer special inducements toward the end of the automotive year in order to sell what the manufacturers have predicted.

    4. Simplify the product line. The more variety in the product line, the more room for error.

    5. Standardize products and processes. This means that “customization” occurs close to final assembly. The basic components are identical, or similar, for all components. Figure 8.14 shows this graphically.

    6. Forecast more accurately. Make forecasts using a well thought out, well controlled process.