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Forecasting As a Tool for Decision Making Forecasting as a Tool for Decision Making Joel Fingennan Roosevelt University Introduction Some Illustrative Numbers For illustration, let us imagine that the manufacturer's 1 Forecasting with the SAS system can be very effective needed raw material is plastic and that the current price for this and efficient. There are a variety of forecasting models available particular plastic ~ 82 cents ~ pound. And that the inventory for the forecast analyst. Ultimately though, forecasting is a tool, carrying charge is ~ cent per pound per month. C~nsequently, if not an end, for decision making. Thus, it is the plan of this the manufacture were to purchase now the cost IS 83 = 82 + 1 paper to show how SAS forecasts may be integrated into a per pound for use in two months: The manufacturer requires decision making framework. 20,000 pounds of this plastic so has budgetted $16,600 to be able to purchase the plastic immediately if necessary. Why Forecast? Thus, for the manufacturer, if the future price 2f the plastic i§ greater than -83 cents ~ .QQ..!!.lli! then the plastic should A key to successful business operations, planning and be purchased now and stored for later use. If the future price 2f strategy is the use of business foreeasts. Since business planning the plastic equal 12. QI less than 83 cents !!IT. pound, then, the and strategy entail decisions or actions at the present time which manufacturer will purchase the plastic later. Figure 1 illustrates will have consequences in the future, useful forecasts about futUre the data on price as a time series over the last three years. uncertain events are essential. Business forecasts are thus an important source of information for management. Using an ARIMA model for forecasting, we produce a price forecast for the next 12 months. Figure 2 illustrates the The need for business forecasting is found in all areas forecast and the upper and lower confidence intervals of the and at all levels of business. Often it is the sales forecast which forecast. Figure 3 is an enlarged graph of the forecast. Figure 4 plays a crucial role in production planning. A sales (or demand) is the enlarged graph with the monthly price forecasts starred forecast will provide information regarding capacity planning, along with the current price level noted. product mix, budgets, advertising and promotion. Notice the manner in which the forecast is illustrated. Besides demand forecasting it is often important to We have not plotted the fitted values (in this case, the one-step forecast prices. The prices of raw materials, the prices of ahead forecasts) with the actuals, the in-sample forecast. supplies and required products, competitor prices, and general Naturally, the in-sample forecast will be quite accurate. It will market prices are all items to be forecasted. be much more accurate than the out-of-sample forecast, and thus As we see, forecasting is not an end onto itself, but misleading as to the accuracy of the out-of-sample forecast. We always a integral part of planning, strategy and operations. recommend that only the future forecast values and the confidence interval of forecast be plotted along with the original data. A Simple Example The forecasted future price for February is 83.4 per pound. Then, according to the decision criteria, the Let us suppose a manufacturer is deciding when to buy manufacturer would buy the plastic now rather than wait and some raw material for future production. The choice is between purchase later. purchasing the raw material ~ and storing it in inventory for later use, or purchasing the raw material later for the future production. We shall simplify this decision to the issues of the Yet, all Forecasts are Wrong! current cost of the raw material, the inventory costs, and the future cost of the raw material. Since the inventory costs are It is unlikely that any business forecast is perfect. We known and stable, the forecasting issue is the forecast of the always remember the advice of that great business forecaster, future cost of the raw material. Casey Stengel, who said, "Never make predictions, especially about the future." Indeed, with any good business forecast a In the simplest of terms, if the forecast of the futUre cost confidence interval around that forecast also should be supplied. of the raw material is sufficiently higher than current cost, then Thus, the forecast analyst provides a confidence interval of it is prudent for the decision maker to purehase the raw material forecast in addition to the actual point forecast. The SAS now and store it in inventory for later use. If the forecasted system provides, either by default or by option, confidence future price of the raw material is either equal to or lower than intervals of forecast. These are illustrated by the upper and the current price, then it is prudent for the decision maker to lower confidence intervals in Figures 2, 3 and 4. purchase the raw material at the later time. If the data has been properly modelled by ARIMA then there will be a normal distribution around the forecasted price of 83.4, and since SAS provides the standard error of forecast we can easily construct the probability distribution of the February lSAS is a registered trademark of the SAS Institute Inc., Forecast. This is illustrated in Figure 5. C",y, NC USA. 187 In this setting the manufacturer's strategy is not entirely having $16,600 for two months would net about $275. In other dear. The manufacturer intended to buy the plastic now since words, it would cost the manufacture $275 in lost interest if the the forecasted price is 83.4. However, given the forecast purchase at 83 cents per pound is made in January rather than a confidence interval it is possible that the price will be less than purchase at 83 cents per pound is made two months later. 83 per pound, in which case it is better to buy later. Similar arguments can be made about the cost of money With a normal probability distribution of the forecast it and inventory costs if the February price is only 82 cents per is now easy to assign a probability of the price being greater than pound. In which case the manufacturer lose $475, and so on. or equal to 83 cents per pound (Figure 6). In this example, we We thus amend Table 1 with a series of loss/gain values when compute that the probability of the future price being greater comparing the purchase now at 83 cents per pound to a future than or equal to 83 cents per pound is roughly 64%. purchase at various prices. Using PROe CHART the normal distribution may be converted to a discrete distribution as shown by Figure 7. This Table 1 amended way discrete prices may be computed with their probabilities. Table 1 below lists the discrete values and their probabilities. February Probability Loss/Gain Table 1 Prices 79 cents .005 $1,075 Loss February Probability 80 .010 875 Prices 81 .060 675 82 .170 475 79 cents .005 83 .280 275 80 .010 84 .270 425 Gain 81 .060 85 .140 575 82 .170 86 .050 725 83 .280 87 .010 875 84 .270 85 )40 86 .050 87 .010 Using simple expected value calculations we find that the expected value under all the price senatios is a $28 Gain. Again, we conclude that it preferable to buy now rather than buy later. Figure 8 is a graph of the probabilty distribution of the February forecasted -and the Loss/Saving function overlayed using the PLOT2 function in SAS GRAPH. The Loss/Saving function is centered at 83 cents per pound and is asymmetrical. In most settings the a Cost Function is asymmetrical in that the risks associated with forecast error are generally not symmetrical. Indeed, in some cases the asymmetry is essentially zero on one The Decision Making Framework side. At this point we have supplied the decision maker with The point to this paper is thus that forecasts should not be potential February prices for this raW material and their used in isolation but must be integrated into some decision making frame in order for the forecasts to be effectively used. probabilities of occuring. We have suggested, based on this analysis that the raw material be purchased !!illY. rather than later because of the forecasted future price. Purchasing now at 82 cents per pound plus 1 cent per pound for carrying cost during the next two months brings the total cost to 83 cents per pound now, or $16,600 for the 20,000 pounds of raw material. Suppose, two months later the price is 83 cents a pound, so that the manufacture could buy the raw material then at 83 cents per pound. That would be an outlay of $16,600 two months later. Consequently, if the purchase could be delayed for two months, the manufacturer would have the money for other uses or just remaining to gain interest. Let us suppose that the current cost of money is 10% per annum so that 188 FIGURE 1 PMceData 1-- 1-- -1-' 1 r-rI . I I I . i I I I ---j--I1 ' HJ . I I , I I ! I I ' I I 10- -1- I I l r-I i I I ! I I +. -+ -I I ! I I eo , -+---I I I , f- I i-I i, I I 1 , . , I I I .' I. I I 7o+---L-I- 1- 1-+-1 I- I I I l i JAN .. JANOJ JANe. JANe5 JANe6 JAN87 JANeS JANe.
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