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Operations Management Assignment

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Submitted By dodofigo
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Question 1: a) Learning curve equation:
Y(u) = au-b u | Y(u) | Ln(u)x | Ln(Y(u))y | x2 | xy | 13 | 276 | 2.565 | 5.620 | 6.579 | 14.415 | 29 | 198 | 3.367 | 5.288 | 11.337 | 17.805 | 41 | 171 | 3.714 | 5.142 | 13.794 | 19.097 | 71 | 137 | 4.263 | 4.919 | 18.173 | 20.969 | 127 | 107 | 4.844 | 4.673 | 23.464 | 22.636 | | Sum: | 18.753 | 25.642 | 73.347 | 94.922 | x = 18.7535 = 3.751 y = 25.6425 = 5.128 m = 594.922-[18.75325.642]573.347-(18.753)2 = -0.415 c = 5.128 – (-0.415)(3.751) = 6.685 a = e6.685 = 800.311 b = -m = 0.415
Y(u) = 800.31u-0.415 b) Average learning rate:
L = 2-b = 2-0.415 = 0.750
L = 75% c) Cost for the 200th unit:
Y(200) = 800.31(200)-0.415 = $88.78

Question 2: a) Values of k and a: y = (xD) f(y) = kya f(1.75y) = k(1.75y)a f(1.75y) = 1.5f(y)
1.5 = f(1.75y)f(y)= k(1.75y)akya=1.75ayaya = 1.75a 1.75a = 1.5 a = log 1.5log 1.75 = 0.725
30 million = k(300,000)0.725 k = 3,207.81 b) Optimal timing of plant additions: a=rxerx-1 r = 12.25%
Using figure 1.4 in the lecture notes plus trial and error to estimate rx. rx = 0.61
0.61e0.61-1=0.7258
x = rxr x = 0.610.1225 = 4.979
Optimal timing of plant additions is 4.98 years c) Optimal size of each plant addition:
D = 25,000 tonnes xD = 4.979 x 25,000 = 124,475
Optimal size of each plant addition is 124,475 tonnes d) Optimal cost of each plant addition: f(25,000) = 3,207.81(25,000)0.725 = 4,951,253.281
Optimal cost of each plant addition is $4.95 million e) Sum of present costs:
Cx= k(xD)a1-e-rx
C4.979=3,207.81(4.979 x 25,000)0.7251-e-0.61= 34,691,812
Sum of present costs is $34.69 million
Question 3: a) February 2012 forecast, MAD – 2 months SMA:
FFeb 2012= DJan+D(Dec)2= 144+1342=139
FJan= DDec+D(Nov)2= 134+1262=130
FDec= DNov+D(Oct)2= 126+1172=121.5 Month | Dt | Ft | Et | |Et| | December, 2011 | 134 | 130 | -4 | 4

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