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hw6
Course: ECON 20091_ECO, Fall 2008School: USC
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Yildiz Burcu Leon Zhu BUAD 311 311 Operations Management Fall 2007 Homework 6: Forecasting Due 10/30/2007 1. The question asks to determine and n. a. 2/ (n + 1) = 2/ (15 + 1) = 2/16 = 0.125 = b. 2/ (n + 1) = 0.2 0.2n + 0.2 = 2 1.8 = 0.2n n=9 2. Question 18 on page 554 = 0.1 = 0.2 = 0.3 trend est. = -500 level est. = 20500 seasonal est. = 1.15, 1.4, 0.95, 0.5 Trend Tt = (prior trend) + (1 - ) (past trend...
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Yildiz Burcu Leon Zhu BUAD 311 311 Operations Management Fall 2007 Homework 6: Forecasting Due 10/30/2007 1. The question asks to determine and n. a. 2/ (n + 1) = 2/ (15 + 1) = 2/16 = 0.125 = b. 2/ (n + 1) = 0.2 0.2n + 0.2 = 2 1.8 = 0.2n n=9
2. Question 18 on page 554 = 0.1 = 0.2 = 0.3 trend est. = -500 level est. = 20500 seasonal est. = 1.15, 1.4, 0.95, 0.5 Trend Tt = (prior trend) + (1 - ) (past trend estimator) = 0.2 (-3000) + (0.8) (-500) = -1000 Level Lt = (At-1 / It-1-N) + (1-)(L1 + Tt-1) = 0.1 (15000/0.5) + (0.9)(9000 + -3000) = 8400 Seasonal It = (At-1 / L1) + (1 - ) (Past Seasonal Estimate) = 0.3(15000/9000) + (0.7)(0.5) = 0.85 Mean Demand in Season (19000 + 24000 + 15000) / 3 = 19333.3
Burcu Yildiz Leon Zhu BUAD 311 Forecast F1 = (L1 T1) * It-N = (8400 + 1000) * 0.85 = 7990 for season four this year 3. Camera question a. The question asks to calculate the simple exponential smoothing forecast for the demand for silver cameras in Week 10 At-1 = 2555 Ft-1 = 2348 = 0.4 Ft = Ft-1 + (At-1 - Ft-1) = 2348 + 0.4 (2555 2348) = 2430.8 MADt-1 = At - Ft / n = (2111-1903+ 1805 - 2111 + 2010 - 1805 + 2222 2010+ 2435 - 2222+ 2113 - 2435 + 2348 - 2113 + 2555-2348) / 8 = (208 + 306 + 205 + 212 + 213 + 322 + 235 + 207) / 8 = 238.5 MADt = At-1 - Ft-1+ (1 - ) MADt-1 = 0.4 2555 - 2348+ (0.6) * 238.5 = 225.9 b. The question asks to calculate the simple exponential smoothing forecast for the demand for red metallic cameras in Week 10 At-1 = 1589 Ft-1 = 1438 = 0.4 Ft = Ft-1 + (At-1 - Ft-1) = 1438 + 0.4 (1589 1438) = 1498.4
Burcu Leon Yildiz Zhu BUAD 311 MADt-1 = At - Ft / n = (1808-2009+ 1999 - 1808 + 1778 - 1999 + 1567 1778+ 1799 - 1778+ 1665 - 1799 + 1438 - 1665 + 1589-1438) / 8 = (201 + 191 + 221 + 211 + 21 + 134 + 227 + 151) / 8 = 169.63 MADt = At-1 - Ft-1+ (1 - ) MADt-1 = 0.4 1589 - 1438+ (0.6) * 169.6 = 162.175 c. The question asks to calculate the stock needed with the probability of not meeting demand at 0.1 in week 10. Silver MAD = 225.9 Forecast = 2430.8 P (N(2430.8, 1.25 MAD > amt. stocked) P{N(0,1) > (amt. stocked 2430.8) / 1.25 MAD) = 0.01 Thus 2.33*1.25*225.9 + 2430.8 = 3088.73 Red MAD = 162.2 Forecast = 1498.4 P (N(1498.4, 1.25 MAD > amt. stocked) P{N(0,1) > (amt. stocked 1498.4) / 1.25 MAD) = 0.01 Thus 2.33*1.25*162.2 + 1498.4 = 1970.7 d. Asks for the number of basic cameras that should be kept in stock with the probability of not meeting demand at 0.1 in week 10 Ft-1 = 2348 + 1438 = 3786 At-1 = 2555 + 1589 = 4144 Ft = Ft-1 + (At-1 - Ft-1) = 3786 + 0.4(4144 3786) =3929.2
Burcu Yildiz Leon Zhu BUAD 311 MADt-1 = At - Ft / n = (3919 - 3912+ 3804 - 3919 + 3788 - 3804 + 3789 3788+ 4234 - 3789+ 3778 - 4234 + 3786 - 3778 + 4144 - 3786) / 8 = (7 + 115 + 16 + 1 + 456 + 456 + 8 + 358) / 8 = 175.75 MADt = At-1 - Ft-1+ (1 - ) MADt-1 = 0.4 4144 - 3786+ (0.6) * 175.75 = 248.65 P (N(3929.2, 1.25 MAD > amt. stocked) P{N(0,1) > (amt. stocked 3929.2) / 1.25 MAD) = 0.01 Thus 2.33*1.25*248.65 + 3929.2 = 4653.4 Combined stock from part c 3088.73 + 1970.7 = 5059.43 Answer: The number is less than the combined answers from part c.
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