forecasting assignment

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The text book we are using is.. wink, Melnyk, Cooper & Hartley, (2017), Managing Operations Across the Supply Chain, McGraw Hill, 3rd Edition.

Question 8 page 435
The owner of an online video rental service has recorded the following rentals each week:
Week 1 2 3 4 5 6 7 8
Rentals 1202 1503 1444 1254 1609 1499 1689 1555
Use a three-week moving average to forecast sales for each of the weeks 4 through 9.
For the prediction of rentals of week 9 using a three week moving average, then:
1499+1689+15553=1581 rentalsFor week 8:
1609+1499+16893=1599 rentalsFor week 7:
1254+1609+14993=1454 rentalsFor week 6:
1444+1254+16093=1435 rentalsFor week 5:
1503+1444+12543=1400 rentalsFor week 4:
1202+1503+14443=1383 rentalsUse a four-week moving average to forecast sales for each of the weeks 5 through 9.
Using a four moving average, the rentals for week 9 through 5 are obtained as:
1609+1499+1689+15554=1588 rentals1689+1499+1609+12544=15121444+1254+1609+14994=14511503+1444+1254+16094=14521202+1503+1444+12544=1350Compare the forecasts created by these two methods using mean absolute deviation. Which forecasting method would you recommend?
3-week moving average
Week Actual Rentals Predicted Value Difference
1 1202    
2 1503    
3 1444    
4 1254 1383 129
5 1609 1400 209
6 1499 1435 64
7 1689 1454 235
8 1555 1599 44
    Sum of Difference 681
    Average Difference 136.2
4-week moving average
Week Actual Rentals Predicted Value Difference
1 1202    
2 1503    
3 1444    
4 1254    
5 1609 1350.

75 258
6 1499 1452.5 47
7 1689 1451.5 238
8 1555 1512.75 42
    Sum of Difference 585
    Average Difference 146
Since the 3 week moving average has a smaller MAD, then it is better for forecasting this data.
Question 9 page 436
A ski repair shop at a resort in Colorado sells replacement poles each season. The shop needs to develop a forecast of next season’s sales so that it can place an order for poles with its supplier well in advance of the beginning of the season. Sales data for the past five years are shown below. 
Year 1 2 3 4 5
Sales (units) 375 395 360 400 380
Develop and compare the forecasts given by the following models:
A five-year moving average model.
The sales in the 6th week may be predicted as:
375+395+360+400+3805=382 salesA weighted moving average model with weights of 0.1, 0.1, 0.2, 0.3, and 0.3 for years 1 through 5, respectively.
For year 1 through 5:
375×0.30.3=375375×0.3+395×0.30.3+0.3=385375×0.3+395×0.3+360×0.20.3+0.3+0.2=378375×0.3+395×0.3+360×0.2+400×0.10.3+0.3+0.2+0.1=381375×0.3+395×0.3+360×0.2+400×0.1+380×0.10.3+0.3+0.2+0.1+0.1=381An exponential smoothing model with a year 1 forecast of 380 and α = 0.2.
Year Sales Forecast
1 375 380
2 395 379
3 360 382
4 400 378
5 380 382
6   382
The exponential smoothening model has values that are a bit closer to each other compared to the other models.
The 5 year moving average can only predict year 6 only.
The weighted average method can only predict up to year 5 only.