Question

Two experienced managers at Wilson Boat Inc. are resisting the introduction of a computerized exponential smoothing system, claiming that their judgmental forecasts are much better than any computer could do. Their past record of predictions is as follows: Week Actual Demand Manager's Forecast 1 3,800 4,400 2 4,100 4,800 3 4,300 3,700 4 3,100 3,800 5 3,900 3,500 6 4,500 3,500 7 5,700 4,900 8 4,000 4,700 9 4,500 3,500 10 4,900 5,400 How would the manager’s forecast compare to a single exponential smoothing forecast using α = 0.8? Do not round intermediate calculations. Round your answers to two decimal places. The MSE value based on the manger’s forecast is __________ The MSE value based on the single exponential smoothing forecast using α = 0.8 is __________ The (single exponential smoothing model, manager's forecast) should be chosen based on MSE value. Find the best single exponential smoothing model by evaluating the MSE from 0.1 to 0.9, in increments of 0.1. Do not round intermediate calculations. Round your answers to two decimal places. Alpha MSE 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 c. The model based on a smoothing constant of ( 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) is the best. How does this model compare with the manager's forecast? d. The (single exponential smoothing model, manager's forecast) has the lowest MSE.

Answer 1

a.

Error^2 Manager's Forecast AB Actual Week Demand Forecast Error 3800 3800 4100 3800 4300 40401 3100 4248 3900 33301 4500 3786) 5700 4357 40001 5431 45001 4286 10 4900 4457 12 MSE 13 Alpha 0.8 14 ایهاباطاه لهاحلعاملة 300 260 - 1148 5701 714 1343 - 1431 214 443 90000 67600 1317904 325356 509910 1803155 2049011 45673 196021 711626 G H Error Error^2 44001 -600 360000 4800 -700| 490000 37001 600 360000 3800 -700 490000 3500 400 160000 3500 1000 1000000 4900 800 640000 47001 -700 490000 3500 1000 1000000 5400 - 500 250000 524000

The MSE value based on the manger’s forecast is 524000

The MSE value based on the single exponential smoothing forecast using α = 0.8 is 711626

The manager's forecast should be chosen based on MSE value

Formula

F Error Week 21 3 2 4 3 5 4 Actual Demand 3800 4100 4300 3100 3900 4500 5700 4000 4500 4900 Forecast 3800 =$B$13*B2+(1-$B$13)*C2 =$B$13*B3+(1-$B$13)*C3 =$B$13*B4+(1-$B$13)*C4 =$B$13*B5+(1-$B$13)*C5 =$B$13*B6+(1-$B$13)*C6 =$B$13*B7+(1-$B$13)*C7 =$B$13*B8+(1-$B$13)*C8 =$B$13*B9+(1-$B$13)*C9 =$B$13*B10+(1-$B$13)*C10 Error^2 Manager's Forecast 4400 =D312 4800 =D412 3700 =D5^2 3800 =D6^2 3500 =D742 3500 =D812 4900 =D942 4700 =D1042 3500 =D1142 5400 =ROUND(AVERAGE(E3:E11),2) I=B3-C3 =B4-C4 =B5-C5 =B6-C6 =B7-C7 =B8-C8 =B9-C9 =B10-C10 =B11-C11 Error =B2-F2 =B3-F3 =B4-F4 =B5-F5 =B6-F6 =B7-F7 =B8-F8 =B9-F9 =B10-F10 =B11-F11 н Error^2 =G242 =G312 =G4-2 =G52 =G642 =G742 =G842 =G942 =G10^2 =G1142 =ROUND(AVERAGE(H2:H11),2) 76 8 7 98 10 9 11 10 12 MSE 13 Alpha 14 20 0.8

b)

Alpha	MSE
0.1	618159.6
0.2	569411
0.3	560264.2
0.4	572977.8
0.5	598304.7
0.6	631293.2
0.7	669386.3
0.8	711625.6
0.9	758496.9

c. The model based on a smoothing constant of 0.3 is the best.
d. the manger's forecast has the lowest MSE