Nahmias Chapter Selected Question Solutions
SOLUTIONS TO SELECTED PROBLEMS FROM NAHMIAS’ BOOK
CHAPTER 2
FORECASTING
2.13 Fcst 1 Fcst 2 Demand Err 1 Err 2 Er1^2 Er2^2 |Err1|
223 210 256 33 46 1089 2116 33 289 320 340 51 20 2601 400 51 430 390 375 -55 -15 3025 225 55 134 112 110 -24 -2 576 4 24 190 150 225 35 75 1225 5625 35 550 490 525 -25 35 625 1225 25 1523.5 1599.166 37.16666 (MSE1 (MSE2) (MAD1)
(Err2( (e1/D(*100 (e2/D((100
46 12.89062 17.96875 20 15.0000 5.88253 15 14.66667 4.00000 2 21.81818 1.81818 75 15.55556 33.33333 35 4.761905 6.66667
32.16666 14.11549 11.61155 (MAD2) (MAPE1) (MAPE2)
2.14 It means that E(ei) ( 0. This will show up by considering
[pic]
A bias is indicated when this sum deviates too far from zero.
2.16 MA (3) forecast: 258.33 MA (6) forecast: 249.33 MA (12) forecast: 205.33
2.17, 2.18, and 2.19.
One-step-ahead Two-step-ahead Month Forecast Forecast Demand e1 e2
July 205.50 149.75 223 -17.50 -73.25 August 225.25 205.50 286 -60.75 -80.50 September 241.50 225.25 212 29.50 13.25 October 250.25 241.50 275 -24.75 -33.50 November 249.00 250.25 188 61.00 62.25 December 240.25 249.00 312 -71.75 -63.00
MAD = 44.2 54.3
The one step ahead forecasts gave better results (and should have according to the theory).
2.20 Month Demand MA(3)
CHAPTER 2
FORECASTING
2.13 Fcst 1 Fcst 2 Demand Err 1 Err 2 Er1^2 Er2^2 |Err1|
223 210 256 33 46 1089 2116 33 289 320 340 51 20 2601 400 51 430 390 375 -55 -15 3025 225 55 134 112 110 -24 -2 576 4 24 190 150 225 35 75 1225 5625 35 550 490 525 -25 35 625 1225 25 1523.5 1599.166 37.16666 (MSE1 (MSE2) (MAD1)
(Err2( (e1/D(*100 (e2/D((100
46 12.89062 17.96875 20 15.0000 5.88253 15 14.66667 4.00000 2 21.81818 1.81818 75 15.55556 33.33333 35 4.761905 6.66667
32.16666 14.11549 11.61155 (MAD2) (MAPE1) (MAPE2)
2.14 It means that E(ei) ( 0. This will show up by considering
[pic]
A bias is indicated when this sum deviates too far from zero.
2.16 MA (3) forecast: 258.33 MA (6) forecast: 249.33 MA (12) forecast: 205.33
2.17, 2.18, and 2.19.
One-step-ahead Two-step-ahead Month Forecast Forecast Demand e1 e2
July 205.50 149.75 223 -17.50 -73.25 August 225.25 205.50 286 -60.75 -80.50 September 241.50 225.25 212 29.50 13.25 October 250.25 241.50 275 -24.75 -33.50 November 249.00 250.25 188 61.00 62.25 December 240.25 249.00 312 -71.75 -63.00
MAD = 44.2 54.3
The one step ahead forecasts gave better results (and should have according to the theory).
2.20 Month Demand MA(3)