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## Forecasting

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**IE 214: Operations Management**Lecture 3 Forecasting KAMAL**EXERCISE 4.3**Solution: a) There is no pattern of any kind**EXERCISE 4.3**Solution:**EXERCISE 4.3**Solution: d) The 3-year moving average method gives better results**EXERCISE 4.5**Solution: (381+368+374)/3 = 374.33 b) (381*0.1)+(368*0.3)+(374*0.6) = 372.9**EXERCISE 4.5**Solution: c) Ft = F t-1 + α(At-1 – Ft-1) ; α = 0.2**EXERCISE 4.8**Given:**EXERCISE 4.8**Solution: 91.3333 a) Ft = (96+88+90)/3 = 91.3333**EXERCISE 4.8**89 b) Ft = (88+90)/2 = 89**EXERCISE 4.8**c) MAD = ∑|At-Ft|/n = 13.5/5 = 2.7**EXERCISE 4.8**d) MSE = ∑(At-Ft)^2/n = 66.75/5 = 13.35**EXERCISE 4.8**e) MAPE = (∑|At-Ft|/At)*100/n = 0.149449*100/5 = 2.98897%**EXERCISE 4.19**Solution: Ft = F t-1 + α(At-1 – Ft-1) F3 = 48 = 50 + α(42 - 50) → -8α = -2 → α = 0.25 F5 = F4 + α(A4 – F4) = 50 + 0.25*(46 - 50) = 49**HW**4.1 4.4 4.14 4.45**EXERCISE 4.20**Given: α = 0.1 , ß = 0.2**EXERCISE 4.20**Solution: • Ft= α(At-1) + (1- α)(Ft-1 + Tt-1) • Tt= ß(Ft - Ft-1) + (1- ß)*Tt-1 • FIT = Ft + Tt**EXERCISE 4.20**65.5 0.1 65.6 • Ft= 0.1*(70) + (0.9)(65 + 0) = 65.5 • Tt= 0.2(65.5 - 65) + (0.8)*0 = 0.1 • FIT = 65.5 + 0.1 = 65.6**EXERCISE 4.21**• MSE= ∑(Error^2)/n = 12.7**EXERCISE 4.26**Given: a= y – b x Y = a + b x = 5 + (20)(5) = 105 ^**EXERCISE 4.26**Solution:**EXERCISE 4.26**Solution: b= (650)-(4)(2.5)(55)/[(30)-(4*(2.5^2))] = 100/5 = 20 a= 55 – (20*2.5) = 5 Y = a + b x = 5 + (20)(5) = 105 ^**HW**4.38 4.48**EXERCISE 4.30**Given: • 1000 radials produced each year. • Production planned to be 1200 radials next year.**EXERCISE 4.30**Solution: 1200 / 4 = 300 radials planned to be sold each season next year 300 * Is = Forecast for next year’s season**EXERCISE 4.30**Solution:**HW PROBLEMS**4.27 4.29