Sample_quiz2_solutions

# Generate forecasts for february march and april month

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table shows the actual sales history for January, February, and March. Generate forecasts for February, March, and April. Month Sales January 890,000 February 800,000 March 825,000 L J = 0.1(890,000) + 0.9(900,000 – 50,000) = 854,000 T J = 0.2(854,000 – 900,000) + 0.8(–50,000) = –49,200 Forecast for Feb: 854,000 – 49,200 = 804,800 L F = 0.1(800,000) + 0.9(854,000 – 49,200) = 804,320 T F = 0.2(804,320 – 854,000) + 0.8(–49,200) = –49,296 Forecast for Mar: 804,320 – 49.296 = 755,024 L M = 0.1(825,000) + 0.9(804,320 – 49,296) = 762,021.6 762,022 T M = 0.2(762,022 – 804,320) + 0.8(–49,296) = –47,896.4 –47,897 Forecast for Apr: 762,022 – 47,897 = 714,125 9

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Problem 7 The Northville Post Office experiences a seasonal pattern of daily mail volume every week. The following data for two representative weeks are expressed in thousands of pieces of mail. Day Week 1 Week 2 Sunday 5 8 Monday 20 15 Tuesday 30 32 Wednesday 35 30 Thursday 49 45 Friday 70 70 Saturday 15 10 Total 224 210 (a) Calculate a seasonal factor for each day of the week. Day Seasonal factor Sunday Monday Tuesday Wednesday Thursday Friday Saturday (b) If the postmaster estimates that there will be 230,000 pieces of mail to sort next week, forecast the volume for each day of the week. Day Forecast Sunday Monday Tuesday Wednesday Thursday Friday Saturday 10
Solution option 1: Get seasonal factors by dividing by average demand in the week: Day Week 1 SF1 Week 2 SF2 Avg SF Sunday 5 5/32 = 0.15625 8 8/30 = 0.26667 0.21146 Monday 20 20/32 = 0.62500 15 15/30 = 0.50000 0.56250 Tuesday 30 30/32 = 0.93750 32 32/30 = 1.06667 1.00209 Wednesday 35 35/32 = 1.09375 30 30/30 = 1.00000 1.04688 Thursday 49 49/32 = 1.53125 45 45/30 = 1.50000 1.51563 Friday 70 70/32 = 2.18750 70 70/30 = 2.33333 2.26042 Saturday 15 15/32 = 0.46875 10 10/30 = 0.33333 0.40104 Total 224 210 Average 224/7 = 32 210/7 = 30 Average daily demand is 230,000/7 = 32,857 Day Calculation Forecast Sunday 0.21146(32,857) 6,948 Monday 0.56250(32,857) 18,482 Tuesday 1.00209(32,857) 32,926 Wednesday 1.04688(32,857) 34,397 Thursday 1.51563(32,857) 49,799 Friday 2.26042(32,857) 74,271 Saturday 0.40104(32,857) 13,177 Solution option 2a: Using the moving average from the book, filling in first Wed. value back to Sunday, and last Wed. value forward to Saturday. Day Value Deseasonalized SF Averaged SFs Forecast Sunday 5 32.00 0.156250 0.205979 6767.8 Monday 20 32.00 0.625000 0.556686 18291.0 Tuesday 30 32.00 0.937500 0.989680 32517.9 Wednesday 35 32.00 1.093750 1.046875 34397.2 Thursday 49 32.43 1.511013 1.505507 49466.4 Friday 70 31.71 2.207207 2.270270 74594.3 Saturday 15 32.00 0.468750 0.401042 13177.0 Sunday 8 31.29 0.255708 Monday 15 30.71 0.488372 Tuesday 32 30.71 1.041860 Wednesday 30 30.00 1.000000 Thursday 45 30.00 1.500000 Friday 70 30.00 2.333333 Saturday 10 30.00 0.333333 11

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Solution option 2b: Using the moving average from the book, filling in avg of first Wed. & Thurs. values back to Sunday, and last Tues. & Wed. values forward to Saturday. Day Value Deseasonalized SF Averaged SFs Forecast Sunday 5 32.21 0.155211 0.205459 6750.8 Monday 20 32.21 0.620843 0.554607 18222.7 Tuesday 30 32.21 0.931264 0.986562 32415.5 Wednesday 35 32.00 1.093750 1.046875 34397.2 Thursday 49 32.43 1.511013 1.496683 49176.5 Friday 70 31.71 2.207207 2.256545 74143.3 Saturday 15 32.00 0.468750 0.399081 13112.6 Sunday 8 31.29 0.255708 Monday 15 30.71 0.488372 Tuesday 32 30.71 1.041860 Wednesday 30 30.00 1.000000 Thursday 45 30.36 1.482353 Friday 70 30.36 2.305882 Saturday 10 30.36 0.329412 12
Problem 8 The XYZ Company has an assembly plant in Cincinnati and its parts plant in Indianapolis. Parts are transported from Indianapolis to Cincinnati using trucks. Each shipment costs \$100. The Cincinnati plant assembles and sells 300 finished products each day and operates 50 weeks a year (working 5 days per week). Part #456 costs \$50 and XYZ Company incurs a holding cost of 20 percent per year. How many of part #456 should XYZ Company put in each shipment? What is the cycle inventory of part #456 at XYZ Company?

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