
Concept explainers
a.
To calculate:The observed weekly sales of ball peen hammers at one of the town hardware shop over an eight week period have been 14, 9, 30, 22, 34, 12, 19, and 23. To get the solution of the one step ahead forecast for weeks through 8.
Introduction:The current forecast is the weighted average of the last forecast and the current value of demand
a.

Answer to Problem 24P
The one step ahead forecast from week 4 to week 8 are F4=17.67, F5= 20.33, F6= 28.67, F7= 22.67, F8= 21.67
Explanation of Solution
Four month average of one step ahead forecast from week 4 to week 8 is calculated below:
Week | Demand | MAD |
1 | 14 | |
2 | 9 | |
3 | 30 | |
4 | 22 | 17.67 |
5 | 34 | 20.33 |
6 | 12 | 28.67 |
7 | 19 | 22.67 |
8 | 23 | 21.67 |
Therefore, one step ahead forecast from week 4 to week 8 are F4=17.67, F5= 20.33, F6= 28.67, F7= 22.67, F8= 21.67.
b.
To calculate:The exponential smoothing forecasts for weeks 4 through 8.
Introduction:
b.

Answer to Problem 24P
Week | Demand | MAD | Exponential Smoothing | MAD | |
1 | 14 | ||||
2 | 9 | ||||
3 | 30 | ||||
4 | 22 | 17.67 | 17.67 | 4.33 | 4.33 |
5 | 34 | 20.33 | 18.32 | 15.68 | 13.67 |
6 | 12 | 28.67 | 20.67 | 8.67 | 16.67 |
7 | 19 | 22.67 | 19.37 | 0.37 | 3.67 |
8 | 23 | 21.67 | 19.31 | 3.69 | 1.33 |
Total | 32.74 | 39.67 |
Explanation of Solution
The exponential smoothing forecasts for weeks 4 through 8 are calculated below:
c.
To calculate: Based on the MAD, to find out the method which did better.
Introduction: Forecasting error can be evaluated using the following formula:
c.

Answer to Problem 24P
Explanation of Solution
MAD for Smoothing constant,
So, the exponential smoothing method is better than moving average method for the five weeks.
d.
To calculate: The exponential smoothing forecast made at the end of week 6 for the sales in week 12.
Introduction: Forecasting error can be evaluated using the following formula:
d.

Answer to Problem 24P
The forecast made through exponential smoothing is in week 6 for sales in week 12 is 20.67.
Explanation of Solution
The exponential smoothing constant forecast made in the week 6 is the same for the demand in week 7 for sales of in week 12. Therefore, the forecast made through exponential smoothing in week 6 for sales in week 12 is 20.67.
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Chapter 2 Solutions
Production and Operations Analysis, Seventh Edition
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