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
Dt=30
Ft=27
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 16 17 18 19 20 21 22 23 24
Reams of paper 253 270 230 253 238 272 222 243 289 238 262 234

a. Compare the effectiveness of two-week, four-week, and six week moving averages.
Which should you use to forecast copier use during the next week?

Week Reams of paper Moving Average for n = 2 MFE MAD
1 232
2 263
3 271 247.5 23.5 23.5
4 248 267 -19 19
5 235 259.5 -24.5 24.5
6 261 241.5 19.5 19.5
7 207 248 -41 41
8 243 234.00 9.00 9
9 237 225.00 12.00 12
10 293 240.00 53.00 53
11 243 265.00 -22.00 22
12 260 268.00 -8.00 8
13 253 251.50 1.50 1.5
14 270 256.5 13.5 13.5
15 230 261.5 -31.5 31.5
16 253 250 3 3
17 238 241.5 -3.5 3.5
18 272 245.5 26.5 26.5
19 222 255 -33 33
20 243 247 -4 4
21 289 232.5 56.5 56.5
22 238 266 -28 28
23 262 263.5 -1.5 1.5
24 234 250 -16 16
25 248 -14 20.5

For week fourth
Week Reams of paper Moving Average for n = 4 MFE MAD
1 232
2 263
3 271
4 248
5 235 253.5 -18.5 18.5
6 261 254.3 6.7 6.7
7 207 253.8 -46.8 46.8
8 243 237.8 5.2 5.2
9 237 236.5 0.5 0.5
10 293 237 56 56
11 243 245 -2 2
12 260 254.00 6.00 6
13 253 258.30 -5.30 5.3
14 270 262.30 7.70 7.7
15 230 256.50 -26.50 26.5
16 253 253.30 -0.30 0.3
17 238 251.50 -13.50 13.5
18 272 247.80 24.20 24.2
19 222 248.30 -26.30 26.3
20 243 246.30 -3.30 3.3
21 289 243.80 45.20 45.2
22 238 256.50 -18.50 18.5
23 262 248.00 14.00 14
24 234 258.00 -24.00 24
25 -19.5 17.5

Week Reams of paper Moving Average for n = 6 MFE MAD
1 232
2 263
3 271
4 248
5 235
6 261
7 207 251.7 -44.7 44.7
8 243 247.50 -4.50 4.5
9 237 244.20 -7.20 7.2
10 293 238.50 54.50 54.5
11 243 246.00 -3.00 3
12 260 247.30 12.70 12.7
13 253 247.20 5.80 5.8
14 270 254.80 15.20 15.2
15 230 259.30 -29.30 29.3
16 253 258.20 -5.20 5.2
17 238 251.50 -13.50 13.5
18 272 250.70 21.30 21.3
19 222 252.70 -30.70 30.7
20 243 247.50 -4.50 4.5
21 289 243.00 46.00 46
22 238 252.80 -14.80 14.8
23 262 250.30 11.70 11.7
24 234 254.30 -20.30 20.3
25 -10.5 19.2

The fourth week moving average has the lowest MAD. Never the less it also has the highest level of Bias, so week fourth is the best option in this case.

b. Compare the performance of the simple exponential smoothing model with smoothing constants of 0.01, 0.05, and 0.25. Assume a forecast for week 1 of 230 reams. Which constant worked best? Exponential 0.25 works best or has the lowest MFE
Reams of paper Exponential Smoothing Alpha=0.01 MFE MAD
232 230.02 1.98 1.98
263 230.04 32.96 32.96
271 230.37 40.63 40.63
248 230.78 17.22 17.22
235 230.95 4.05 4.05
261 230.99 30.01 30.01
207 231.29 -24.29 24.29
243 231.05 11.95 11.95
237 231.17 5.83 5.83
293 231.22 61.78 61.78
243 231.84 11.16 11.16
260 231.95 28.05 28.05
253 232.23 20.77 20.77
270 232.44 37.56 37.56
230 232.82 -2.82 2.82
253 232.79 20.21 20.21
238 232.99 5.01 5.01
272 233.04 38.96 38.96
222 233.43 -11.43 11.43
243 233.32 9.68 9.68
289 233.41 55.59 55.59
238 233.97 4.03 4.03
262 234.01 27.99 27.99
234 234.29 -0.29 0.29 234.29 17.78 21.01

Reams of paper Exponential Smoothing Alpha = 0.05 MFE MAD
232 230.1 1.9 1.9
263 230.20 32.81 32.81
271 231.84 39.16 39.16
248 233.79 14.21 14.21
235 234.50 0.50 0.5
261 234.53 26.47 26.47
207 235.85 -28.85 28.85
243 234.41 8.59 8.59
237 234.84 2.16 2.16
293 234.95 58.05 58.05
243 237.85 5.15 5.15
260 238.11 21.89 21.89
253 239.20 13.80 13.8
270 239.89 30.11 30.11
230 241.40 -11.40 11.4
253 240.83 12.17 12.17
238 241.44 -3.44 3.44
272 241.26 30.74 30.74
222 242.80 -20.80 20.8
243 241.76 1.24 1.24
289 241.82 47.18 47.18
238 244.18 -6.18 6.18
262 243.87 18.13 18.13
234 244.78 -10.78 10.78 244.24 11.78 18.57

Reams of paper Exponential Smoothing Alpha = 0.25 MFE MAD
232 230.5 1.5 1.5
263 230.88 32.13 32.13
271 238.91 32.09 32.09
248 246.93 1.07 1.07
235 247.20 -12.20 12.2
261 244.15 16.85 16.85
207 248.36 -41.36 41.36
243 238.02 4.98 4.98
237 239.27 -2.27 2.27
293 238.70 54.30 54.3
243 252.27 -9.27 9.27
260 249.96 10.04 10.04
253 252.47 0.53 0.53
270 252.60 17.40 17.4
230 256.95 -26.95 26.95
253 250.21 2.79 2.79
238 250.91 -12.91 12.91
272 247.68 24.32 24.32
222 253.76 -31.76 31.76
243 245.82 -2.82 2.82
289 245.12 43.88 43.88
238 256.09 -18.09 18.09
262 251.57 10.43 10.43
234 254.17 -20.17 20.17 249.13 18.63 17.92