Chapter 4 Problems

# Chapter 4 Problems - Week of Pints Used 31-Aug 360 7-Sep...

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Week of Pints Used 31-Aug 360 7-Sep 389 14-Sep 410 21-Sep 381 28-Sep 368 5-Oct 374 a.) 3 week Moving Average: 374.333333 pints b.) 3 Week Weighted Moving Average: Week of Pints Used Weight Computations 31-Aug 360 7-Sep 389 14-Sep 410 21-Sep 381 0.1 38.1 28-Sep 368 0.3 110.4 5-Oct 374 0.6 224.4 12-Oct Forecast 372.9 c.)Exponential smoothing (with a smoothing constant, α = 0.2): Week of Actual Forecast: Ft = Ft-1 + α(At-1 – Ft-1) 31-Aug 360 360 7-Sep 389 360 14-Sep 410 365.80 21-Sep 381 374.64 28-Sep 368 375.91 5-Oct 374 374.33 12-Oct 374.26

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Year Demand Forecast 1 7 7 2 9 7 3 5 7.8 4 9 6.68 5 13 7.608 6 8 9.7648 7 12 9.05888 8 13 10.23533 9 9 11.3412 10 11 10.40472 11 7 10.64283 12 Exponential smoothing (with a smoothing constant, α = 0.4) Forecast: Ft = Ft-1 + α(At-1 – Ft-1) The new forecast is better 1 2 3 0 2 4 6 8 10 12 14 Demnd
4 5 6 7 8 9 10 11 Col- umn B

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Year Mileage 1 3000 2 4000 3 3400 4 3800 5 3700 a) 2 Year Moving Average: 3750 miles b.) Mean Absolute Deviation (MAD) Year Mileage 2 Yr. Moving Avg. Error Abs. Error 1 3000 2 4000 3 3400 3500 -100 100 4 3800 3700 100 100 5 3700 3600 100 100 TOTALS 100 300 MAD 100 C.) 2 Ye:ar Weighted Average Year Mileage 2 Yr. Weight Avg. Error Abs. Error 1 3000 2 4000 3 3400 3600 -200 200 4 3800 3640 160 160 5 3700 3640 60 60 TOTALS 20 420 MAD 140 d.) Exponential Smoothing using α=0.5 and an initial forecast of 3000 for year 1

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Unformatted text preview: Year Mileage Forecast Forecast Er. Error *0.5 New Forecast 1 3000 3000 3000 2 4000 3000 1000 500 3500 3 3400 3500-100-50 3450 4 3800 3450 350 175 3625 5 3700 3625 75 37.5 3663 y x xy x^2 Month # of Accidents January 30 1 30 1 February 40 2 80 4 March 60 3 180 9 April 90 4 360 16 TOTALS 220 10 650 30 AVERAGE 55 2.5 y=55 x=2.5 b= 650-(4*2.5*55)/30-4*(2.5)^2 b= 20 a=y-bx a= 5 The regression line is y=5+20x. The forecast for May is x=5 May = 105 Year SEASON 1 2 3 4 Winter 1400 1200 1000 900 1125 1250 0.90 Spring 1500 1400 1600 1500 1500 1250 1.20 Summer 1000 2100 2000 1900 1750 1250 1.40 Fall 600 750 650 500 625 1250 0.50 Total Avg. Annual Demand 5000 Total Avg. Seasonal Demand 1250 Year 5 expected demand for sailboats= 5600 Expected avg seasonal demand=5600/4= 1400 Seasonal index for spring= 1.20 Expected demand for spring (year 5)= 1680 Avg. (Yr.1-4) Demand (a) Avg. Seas. Demand (b) Seas.Index (a)/(b)...
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