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Forecasting
Answer 1250 = 1042 1.2 (latest actual) (1 ) (previous forecast) = 0.1110422 + 0.9110002 = 1004
a. Deseasonalized actual demand for April = b. Deseasonalized May forecast
c. Seasonalized May forecast
(seasonal index) (deseasonalized forecast) = 0.7110042 = 703
TRACKING THE FORECAST 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.
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. 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
Chapter 8
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
Figure 8.8 Forecast and actual sales with bias.
800 Forecast Actual
700 600
DEMAND
234
500 400 300 200 100 0 0
1
2
3 MONTH
Figure 8.9 Forecast and actual demand with bias.
4
5
6
235
Forecasting
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 January February March* April May
Forecast 100 100 100 100 100
Actual 95 110 155 45 90
Cumulative Forecast 100 200 300 400 500
Cumulative Actual 95 205 360 405 495
*Customer foresaw a possible strike and stockpiled. 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
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
Figure 8.10 Forecast and actual sales without bias.
Chapter 8
120 115 110
DEMAND
236
Forecast
105 100 95
Actual
90 85 80 1
2
3
4
5
6
MONTHS
Figure 8.11 Forecast and actual sales without bias.
that the average forecast was correct and there was no bias. The data are plotted in Figure 8.11.
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 mean absolute deviation: • mean implies an average, • absolute means without reference to plus and minus, • deviation refers to the error:
MAD =
sum of absolute deviations number of observations
237
Forecasting
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
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 Uses of mean absolute deviation. Some of the most important follow.
Mean absolute deviation has several uses.
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
1%
1% 4% −3
15% −2
30% −1
30% 0
15% 1
MEAN ABSOLUTE DEVIATIONS
Figure 8.12 Normal distribution curve.
4% 2
3
238
Chapter 8
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: Tracking signal =
algebraic sum of forecast errors MAD
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
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
1
100
96
2
100
98
3
100
104
4
100
110
Deviation
Cumulative Deviation
Tracking Signal
5
2.5
239
Forecasting
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 be able to devise a contingency plan to cope with the possible extra demand. Safety stock. The data can be used as a basis for setting safety stock. This will be discussed in detail in Chapter 11.
P/D Ratio Because of the inherent error in forecasts, companies that 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 and arrival of raw materials, 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 in Figure 8.13.
