Engineering Management

Planning gives you the luxury of deciding ahead of time what you're going to do.

We can categorize forecasting models in two general ways:  quantitative versus qualitative  time series versus causal

Quantitative models use one or more equations to turn a set of numerical or categorical inputs into a forecast of a value or set of values for one or more variables.

Qualitative models are subjective. They are based on the subjective assessments of individuals, working separately or in groups, rather than on formal equations.

Probably the best-known of the qualitative methods is the Delphi technique. Given the amount of time and the cost required to use the Delphi technique, it is most often used for long-range decisions with significant implications for capital expenditures or the organization's future direction. At the other extreme, a qualitative method sometimes used for annual demand forecasting is the grass-roots method, in which individual salespeople estimate next year's sales for their territories and the results are added up (with or without adjustment for perceived bias) to get sales for the district, the region, and the company.

Time series models are based on extrapolating the historical pattern for the variable of interest into the future. The model's inputs may include all or selected past values of the variable and, possibly, the forecast errors for all or selected past periods. Time series models are most often used for short time frames; they will be our primary focus. Causal models estimate the value of the variable of interest, called the dependent variable, on the basis of a second set of variables, called the independent variables that are believed to determine the value of the dependent variable. For example, a school system can do a very good (but not perfect) job of forecasting its kindergarten enrollment by looking at the number of births five years earlier. (Why might this approach not give a perfect

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forecast?) Two popular modeling techniques for causal models are regression and simulation.

Choosing a Forecasting Method The first, and possibly most important point, is that no forecasting system will be best, or even good, for all possible situations. Choosing an appropriate forecasting method involves matching the characteristics, strengths, and weaknesses of the situation with those of the method.

When considering the situational characteristics, the most important is what is being forecasted. Are we interested in the value of a variable at some point in time; in the time at which a series will change direction; or in the time when some event of particular interest (for example, the next generation of some technology) might occur? Besides this overriding consideration, the other situational characteristics usually considered important include: 1. The time horizon for the forecast, divided generally into short-term (up to about three months), intermediate-term (from three months to two years), or long-term (over two years). These time divisions are somewhat arbitrary and may vary considerably from industry to industry. 2. The level of detail, or how much aggregation there will be. For example, are we talking about a product, a product line, a company's division, or the entire company? 3. The number of items. If we are developing forecasts for thousands of items on a monthly basis, we will probably want a simpler technique than if we are forecasting the demand for only one or two items once or twice a year. 4. The stability of the situation. If we can assume basic patterns that held in the past will continue to hold in the future, we can use a different approach than if we are attempting to deal with a great deal of change.

SHORT-TERM FORECASTING When there is no trend in a time series, a naive (but sometimes useful) short-term forecasting approach is to assume that the value of the variable will be the same next period as it is this period. Of course, this approach ignores the effect of seasonality, if it is relevant, but it also causes the forecasts to jump around from period to period in response to the randomness. One way to compensate for this jumpiness in the forecasts is to use averaging. Two popular time series models for averaging when there is no seasonality1 are the simple moving average (SMA) and simple exponential smoothing (SES). Both forecast the value for next period simply by estimating the height or level of the horizontal line (see Figure D.1a) around which the actual values are randomly scattered.

Simple Moving Average If we could assume that the height of the line around which the actual values are randomly scattered has always been the same, then the simplest way to estimate it and forecast the value for the next period would be to average all past values of the variable. Since we cannot always make this assumption, a reasonable compromise is to use the

By Dr Muhammad Ehsan Ulhaque: Visit http://elearning.alhaque.com for Notes Page 2 Topic 03a: Engineering Management average of the last few periods. This approach is called the simple moving average model. Letting Ft be the forecast for period t and Yt be the actual value, the n-period SMA forecast for period t+1 is:

Example D.1

The demand for a particular type of chairs at Luis's furniture company has been fairly stable. The actual numbers of chairs ordered for the past 18 months are given in Table D.1 and graphed in Exhibit D.1 Table D.1 Monthly Demand for Chairs

Month Demand Month Demand Month Demand

1 122 7 105 13 99 2 90 8 105 14 107 3 131 9 118 15 114 4 87 10 135 16 139 5 123 11 108 17 80 6 127 12 91 18 119

Exhibit D.1 Find the six-month simple moving average forecasts for months 7 and 8. Solution: The six-month SMA forecast for month 7 The six-month SMA forecast for month 8 is: is:

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A comparison of the two equations in this example shows why this model is called a simple moving average. As the period to be forecasted moves up by one, the periods for which the actual values are averaged also move up by one; the oldest data value is dropped and replaced by the new one.

Simple Exponential Smoothing While the simple moving average forecast is easy to compute and the concept is easy to understand, it has two possible drawbacks: (1) it treats all values used equally, regardless of their age, and 2) it requires a fair amount of storage (although this drawback becomes less of a problem as computer storage gets cheaper). An alternative to the SMA model is simple exponential smoothing (SES), which differs from SMA in three important respects: 1. The model implicitly uses the entire past history of the time series, not just the most recent periods. 2. The weights assigned to the values decrease3 with the age of the data, rather than being 1/n for each. 3. Less storage is required: Only the value of the smoothing constant ( in the equations to follow) and the most recent forecast are needed. There are two alternative, but equivalent, forms of the SES model. The first, Ft+1 = Yt + (1- )Ft says that the new forecast is simply a weighted average of the most recent actual value, Yt, and the old forecast, Ft.

The smoothing constant, , is a number between 0 and 1. A value close to 0 produces a lot of smoothing (similar to a large value for n in an SMA model), while a value close to 1 yields a forecast that responds quickly to changes in the data pattern. Values of α close to unity have less of a smoothing effect and give greater weight to recent changes in the data, while values of α closer to zero have a greater smoothing effect and are less responsive to recent changes. There is no formally correct procedure for choosing α. Sometimes the statistician's judgment is used to choose an appropriate factor. Alternatively, a statistical technique may be used to optimize the value of α. By doing a little algebra on the equation above, we get the second form of the equation: Ft+1 = Ft + (Yt – Ft). This equation shows that the new forecast is simply the old forecast corrected by a percentage of the amount by which that forecast was in error (Yt – Ft). Just as the n-period SMA model could not produce a forecast before period n+1, so the SES model cannot give a forecast for period 1 unless, for some reason, there are values for F0 and Y0. Common practice, then, is to let F1 = Y1 and start the forecasts with t = 2.

Example D.2

Refer to Example D.1. Find the SES forecasts for months 2 and 3. Use = .3. Solution: Letting F1 = Y1 = 122 (from Table D.1), the SES forecast for chairs in period 2 with = .3 is: F2 = Y1 + (1– )F1 = (.3)(122) + (.7)(122) = 122 The forecast for period 3 is: F3 = Y2 + (1– )F2 = (.3)(90) + (.7)(122) = 112.4

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As with the SMA model, the simple form of the SES model is easy to automate with a spreadsheet, either by building the equation into the sheet directly or by using the spreadsheet's built-in procedure. Exhibit D.3 shows the results of applying the exponential smoothing procedure from data analysis in Excel to the data in Table D.1. As with the graph for the SMA model, note that the SES forecasts are much less variable than the actual data. With a smaller value for , there would be even less variability.

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