Problems Chapter 12

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Problems Ch. 12
Problem 2
2. Given the series of demand data below
Period 1 2 3 4 5 6 7 8 9 10
Demand 40 33 56 43 23 45 38 40 29 40

a. Calculate the forecast for periods 7 through 11 using moving average models with n=2, n=4, and n=6
b. Calculate the bias and MAD for each set forecasts. Which moving average model is best?
Table for n=2
Period Demand Moving Average for n=2 MFE MAD
1 40
2 33
3 56
4 43
5 23
6 45
7 38 34 4 4
8 40 41.5 -1.5 1.50
9 29 39 -10 10.00
10 40 34.5 5.5 5.50
11 34.5 -2 21.00

Period Demand Moving Average for n=4 MFE MAD
1 40
2 33
3 56
4 43
5 23
6 45
7 38 41.75 -3.75 3.75
8 40 37.25 2.75 2.75
9 29 36.5 -7.5 7.5
10 40 38 2 2
11 36.75 -6.5 16 Table for n= 4

Table for n=6
Period Demand Moving average for n=6 MFE MAD
1 40
2 33
3 56
4 43
5 23
6 45
7 38 40 -2 2
8 40 39.67 0.33 0.33
9 29 40.83 -11.83 11.83
10 40 36.33 3.67 3.67
11 35.83 -9.83 17.83

Which moving average model is best?
Table for n=2 is the best option because is the one forecast that has the lower % of error

Problem 3
3. If last period’s forecast was 27 and the demand was 30, what was the forecast error? What would be forecast for the next period using an exponential smoothing model with alpha=.5?
Dt -Ft = Forecast error
Forecast error=30-27= 3
Ft+1 = α dt + (1- α) Ft
Ft+1 = (.5) (30) + (1-.5) 27
Ft+1 = 15+ .5 (27)
Ft+1 = 15+ 13.5
Ft+1 = 28.5

Problem 5
5. You have become concerned about the amount of copier paper used in your office after repeatedly running out of supplies. Your assistant keeps track of the number of reams (packages of 500 sheets) for 24 weeks:

Week 1 2 3 4 5 6 7 8 9 10 11 12
Reams of paper 232 263 271 248 235 261 207 243 237 293 243 260
Week 13 14 15…...

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