Forecasting Efficient operations require that managers match supply to demand. A
ID: 3338444 • Letter: F
Question
Forecasting
Efficient operations require that managers match supply to demand. As they lack a crystal ball, they must rely on forecasting to help predict future demand. Forecasts then drive decisions regarding purchasing, production, and logistics—the key activities in the order fulfillment process. Since most forecasting methods rely on historical data to predict future behavior and are our “best guess,” they are almost always wrong. Even so, in the absence of perfect information, good forecasts can improve the quality of our decision-making. Three types of simple forecasts—simple moving average, weighted moving average, and exponential smoothing—are described below.
• Simple Moving Average: Uses the average of recent time periods to estimate the next period’s demand. Using more time periods, increasing stability. Using fewer time periods, increases responsiveness.
• Weighted Moving Average: More recent data may better reflect future behavior. Managers acknowledge this by weighting recent time periods more highly. Managerial judgment (and measurement of forecast error) is used to identify the number of periods and set appropriate weights. Weights must add up to 1.0.
• Exponential Smoothing: Sometimes unexpected, and largely random, spikes in demand may occur. To avoid being overly influenced by these spikes, managers may use exponential smoothing, which weights the last period’s demand with the last period’s forecast. Manager choose a smoothing constant based on whether they have more faith in the actual demand or the previous period’s forecast. The formula for exponential smoothing is as follows: Forecastt+1 = aActual Demandt + (1-a)Forecastt
Because forecasts tend to be wrong, it is important to measure how wrong—and then to make adjustments to improve the forecasting process. Depending on the industry, forecast errors are often 30 - 80%. Two basic approaches—mean squared error and mean absolute error—are described below.
• Mean Squared Error: Is the average of all the squared errors. The result is not very intuitive.
• Mean Absolute Deviation: Is the average of absolute values of the difference between the actual and forecast values. Taking the absolute value prevents high and low forecasts from canceling each other out.
Problems:
Using the numbers in the chart below, calculate the following:
Your Answers
1. Three-period moving average:
2. Four-period weighted moving average (weights: p1=.1, p2=.2, p3=.3, p4=.4):
3. Smoothed forecast for Period 6 (use an a = .3):
4. Mean Squared Error for Periods 1-5:
5. Mean Absolute Deviation for Periods 1-5:
6. Average percent error for Periods 1-5:
Period
Actual Demand
Forecast Demand
Error
(You must calculate)
Squared Error
(You must calculate)
Absolute Deviation
(You must calculate)
Percent Error
(You must calculate)
1
48
52.69
2
45
48.97
3
47
45.82
4
45
46.76
5
40
45.36
Period
Actual Demand
Forecast Demand
Error
(You must calculate)
Squared Error
(You must calculate)
Absolute Deviation
(You must calculate)
Percent Error
(You must calculate)
1
48
52.69
2
45
48.97
3
47
45.82
4
45
46.76
5
40
45.36
Explanation / Answer
Period Demand 3pt WMA Exp_Smoothing 3pt_dev 3pt_dev_abs 3pt_dev_abs^2 MAPE 3pt WMA_dev WMA_dev_abs WMA_dev_abs^2 MAPE WMA Exp_Smoothing_dev Exp_Smoothing_dev_abs Exp_Smoothing_dev_abs^2 MAPE Exp_Smoothing 1 48 48 0 0 0 0.00% 2 45 46.66666667 48 -1.666666667 1.666666667 2.777777778 3.70% -3 3 9 6.67% 3 47 45.66666667 45.9 47.1 1.333333333 1.333333333 1.777777778 2.84% 1.1 1.1 1.21 2.34% -0.1 0.1 0.01 0.21% 4 45 44 43.4 47.07 1 1 1 2.22% 1.6 1.6 2.56 3.56% -2.07 2.07 4.2849 4.60% 5 40 46.449 -6.449 6.449 41.589601 16.12% 6 44.5143 MAD for 3pt MSE MAPE MAD for WMA MSE MAPE MAD for Exp_Smoothing MSE MAPE 1.333333333 1.851851852 2.92% 1.35 1.885 2.95% 2.3238 10.9769002 5.52%
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