### Forecasting as a Tool for Decision Making

*Joel Fingennan Roosevelt University*

Introduction

Forecasting with the SAS1 system can be very effective and efficient. There are a variety of forecasting models available

for the forecast analyst. Ultimately though, forecasting is a tool,

not an end, for decision making. Thus, it is the plan of this

paper to show how SAS forecasts may be integrated into a

decision making framework.

Why Forecast?

A key to successful business operations, planning and

strategy is the use of business foreeasts. Since business planning and strategy entail decisions or actions at the present time which

will have consequences in the future, useful forecasts about futUre uncertain events are essential. Business forecasts are thus an

important source of information for management.

The need for business forecasting is found in all areas and at all levels of business. Often it is the sales forecast which plays a crucial role in production planning. A sales (or demand) forecast will provide information regarding capacity planning, product mix, budgets, advertising and promotion.

Besides demand forecasting it is often important to forecast prices. The prices of raw materials, the prices of supplies and required products, competitor prices, and general market prices are all items to be forecasted.

As we see, forecasting is not an end onto itself, but always a integral part of planning, strategy and operations.

A Simple Example

Let us suppose a manufacturer is deciding when to buy some raw material for future production. The choice is between 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 current cost of the raw material, the inventory costs, and the future cost of the raw material. Since the inventory costs are known and stable, the forecasting issue is the forecast of the future cost of the raw material.

In the simplest of terms, if the forecast of the futUre cost of the raw material is sufficiently higher than current cost, then it is prudent for the decision maker to purehase the raw material now and store it in inventory for later use. If the forecasted future price of the raw material is either equal to or lower than the current price, then it is prudent for the decision maker to purchase the raw material at the later time.

lSAS is a registered trademark of the SAS Institute Inc., C",y, NC USA.

Some Illustrative Numbers

For illustration, let us imagine that the manufacturer's
needed raw material is *plastic and that the current price for this *

particular plastic ~ 82 cents ~ pound. And that the inventory carrying charge is ~ cent per pound per month. C~nsequently, if the manufacture were to purchase now the cost IS 83 = 82

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1 per pound for use in two months: The manufacturer requires 20,000 pounds of this plastic so has budgetted $16,600 to be able to purchase the plastic immediately if necessary.Thus, for the manufacturer, if the future price

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the plastic*i§*greater than -83 cents ~

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then the plastic should be purchased now and stored for later use. If the future price### 2f

the plastic equal 12. QI less than 83 cents !!IT. pound, then, the manufacturer will purchase the plastic later. Figure 1 illustrates the data on price as a time series over the last three years.Using an ARIMA model for forecasting, we produce a price forecast for the next 12 months. Figure 2 illustrates the forecast and the upper and lower confidence intervals of the forecast. Figure 3 is an enlarged graph of the forecast. Figure 4 is the enlarged graph with the monthly price forecasts starred along with the current price level noted.

Notice the manner in which the forecast is illustrated. We have not plotted the fitted values (in this case, the one-step ahead forecasts) with the actuals, the in-sample forecast. Naturally, the in-sample forecast will be quite accurate. It will

be much more accurate than the out-of-sample forecast, and thus misleading as to the accuracy of the out-of-sample forecast. We recommend that only the future forecast values and the confidence interval of forecast be plotted along with the original data.

The forecasted future price for February is 83.4 per pound. Then, according to the decision criteria, the manufacturer would buy the plastic now rather than wait and purchase later.

Yet, all Forecasts are Wrong!

It is unlikely that any business forecast is perfect. We always remember the advice of that great business forecaster, Casey Stengel, who said, "Never make predictions, especially about the future." Indeed, with any good business forecast a confidence interval around that forecast also should be supplied. Thus, the forecast analyst provides a confidence interval of forecast in addition to the actual point forecast. The SAS system provides, either by default or by option, confidence intervals of forecast. These are illustrated by the upper and lower confidence intervals in Figures 2, 3 and 4.

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 Forecast. This is illustrated in Figure 5.

In this setting the manufacturer's strategy is not entirely dear. The manufacturer intended to buy the plastic now since the forecasted price is 83.4. However, given the forecast confidence interval it is possible that the price will be less than 83 per pound, in which case it is better to buy later.

With a normal probability distribution of the forecast it is now easy to assign a probability of the price being greater than or equal to 83 cents per pound (Figure 6). In this example, we compute that the probability of the future price being greater than or equal to 83 cents per pound is roughly 64%.

Using PROe CHART the normal distribution may be

converted to a discrete distribution as shown by Figure 7. This way discrete prices may be computed with their probabilities. Table 1 below lists the discrete values and their probabilities.

Table 1 February Probability Prices 79 cents .005 80 .010 81 .060 82 .170 83 .280 84 .270 85 )40 86 .050 87 .010

The Decision Making Framework

At this point we have supplied the decision maker with potential February prices for this raW material and their 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

having $16,600 for two months would net about $275. In other words, it would cost the manufacture $275 in lost interest if the purchase at 83 cents per pound is made in January rather than a purchase at 83 cents per pound is made two months later.

Similar arguments can be made about the cost of money and inventory costs if the February price is only 82 cents per pound. In which case the manufacturer lose $475, and so on. We thus amend Table 1 with a series of loss/gain values when comparing the purchase now at 83 cents per pound to a future purchase at various prices.

Table 1 amended

February Probability Loss/Gain Prices 79 cents .005 $1,075 Loss 80 .010 875 81 .060 675 82 .170 475 83 .280 275 84 .270 425 Gain 85 .140 575 86 .050 725 87 .010 875

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 side.

The point to this paper is thus that forecasts should not

be used in isolation but must be integrated into some decision making frame in order for the forecasts to be effectively used.

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**FIGURE 5 **

### Probability Distribution of February Forecast

**Forecast = ** **B3A cents. Standard Error 01 Forecast ****= 1.89 **

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### Probability Distribution of February Forecast

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