Problem 1. Sales for the past 12 months at Dalworth Company are given here.
|
Month
|
Sales ($ millions)
|
Month
|
Sales ($ millions)
|
|
January
|
20
|
July
|
53
|
|
February
|
24
|
August
|
62
|
|
March
|
27
|
September
|
54
|
|
April
|
31
|
October
|
36
|
|
May
|
37
|
November
|
32
|
|
June
|
47
|
December
|
29
|
a. Use a three-month moving average to forecast the sales for the months May through December.
b. Use a four-month moving average to forecast the sales for the months May through December.
c. Compare the performance of the two methods by using the mean absolute deviation as the performance criterion. Which method would you recommend?
d. Compare the performance of the two methods by using the mean absolute percent error as the performance criterion. Which method would you recommend?
Problem 2. Karl’s Copiers sells and repairs photocopy machines. The manager needs weekly forecasts of service calls so that he can schedule service personnel. Use the actual demand in the first period for the forecast for the first week so error measurement begins in the second week. The manager uses exponential smoothing with a = 0.20. Forecast the number of calls for week 6, which is next week.
|
Week
|
Actual Service Calls
|
|
1
|
24
|
|
2
|
32
|
|
3
|
36
|
|
4
|
23
|
|
5
|
25
|
a. Use a three-month moving average to forecast the sales for the months May through December.
b. Use a four-month moving average to forecast the sales for the months May through December.
c. Compare the performance of the two methods by using the mean absolute deviation as the performance criterion. Which method would you recommend?
d. Compare the performance of the two methods by using the mean absolute percent error as the performance criterion. Which method would you recommend?
Problem 3. The demand for Krispee Crunchies, a favorite breakfast cereal of people born in the 1940s, is experiencing a decline. The company wants to monitor demand for this product closely as it nears the end of its life cycle. The following table shows the actual sales history for January – October. Generate forecasts for November – December, using the trend projection by regression method.
|
Month
|
Sales
|
Month
|
Sales
|
|
January
|
890,000
|
July
|
710,000
|
|
February
|
800,000
|
August
|
730,000
|
|
March
|
825,000
|
September
|
680,000
|
|
April
|
840,000
|
October
|
670,000
|
|
May
|
730,000
|
Nov n November
|
|
June
|
780,000
|
December
|
Problem 4. The manager of Snyder’s Garden Center must make the annual purchasing plans for rakes, gloves, and other gardening items. One of the items the company stocks is Fast-Grow, a liquid fertilizer. The sales of this item are seasonal, with peaks in the spring, summer, and fall months. Quarterly demand (in cases) for the past 2 years follows:
|
Quarter
|
Year 1
|
Year 2
|
|
1
|
40
|
60
|
|
2
|
350
|
440
|
|
3
|
290
|
320
|
|
4
|
210
|
280
|
|
Total
|
890
|
1,100
|
If the expected sales for Fast-Grow are 1,150 cases for year 3, use the multiplicative seasonal method to prepare a forecast for each quarter of the year.
Problem 5. The manager of a utility company in the Texas panhandle wants to develop quarterly forecasts of power loads for the next year. The power loads are seasonal, and the data on the quarterly loads in megawatts (MW) for the last 4 years are as follows:
|
Quarter
|
Year 1
|
Year 2
|
Year 3
|
Year 4
|
|
1
|
103.5
|
94.7
|
118.6
|
109.3
|
|
2
|
126.1
|
116.0
|
141.2
|
131.6
|
|
3
|
144.5
|
137.1
|
159.0
|
149.5
|
|
4
|
166.1
|
152.5
|
178.2
|
169.0
|
The manager estimates the total demand for the next year at 600 MW. Use the multiplicative seasonal method to develop the forecast for each quarter.