Utility Theory

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Production Information and Decision Systems Final
Presentation
Utility Theory ?????????????
????????? ???????????
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Goal?? Optimal Operation Point
Indifference Curve
Cycle Time (better gt)
Optimal Operation Point
Option Curve
Throughput (better gt)
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??Option Curve????? ????Throughput? Cycle
Time?Data,???????????oc(x)
??????? ????Throghput?????Cycle Time???????W
??????????,oc(x)????,??Lagrange?????????
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? Queuing Capacity Model ?????????,????? scatter
diagram ,????????????
Cycle Time (better gt)
Throughput (better gt)
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????????????
???????,???????????????

• ?????
• ?????
• ?????
• ????

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??????????
??
?? 1. MSE 0.053399 2. ???????????? 3.???
Option Curve ?????
Cycle Time (better gt)
Throughput (better gt)
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??????????
??
?? 1. MSE 0.011198 2.?????????????
,??????????
Cycle Time (better gt)
Throughput (better gt)
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??????????
??
?? 1. MSE 0.002379 2. ??????,?????
Cycle Time (better gt)
Throughput (better gt)
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?????????
??
?? 1.MSE 0.0099569 2.???????,?????
Cycle Time (better gt)
Throughput (better gt)
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???????
Throughput ???? UTH
Cycle Time ???? UCT
??????
????? U
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????????????
Indifference Curves
Option Curve
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Lagrange ???????
????????? U(x,y)
???? OCE(x,y) 0 OC(x) - y
Lagrange??
??????????? x, y

• ?????
• ?(x,y)???????
• ?? m ???? n ?? ??,??????

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Optimal Operation Point ????
?????? Throughput (ST) 8760 wafers
(SA) 13080 wafers Cycle Time
(ST) 2009.40 hours (SA)
591.06 hours
Optimal operation point (x,y)(0.68,0.69)
??????? Throughput ST x ( ST SA )
11770.61 wafers Cycle
Time ST y ( ST SA )
1040.80 hours
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??????????????????
Let yOC(x) be option curve Let
u(x)U(x,y)U(x,OC(x))UTH(x)UCT(OC(x)) By
Chain Rule
Let
Solve x first, then compute y and U by OC(x) and
U(x,y) respectively
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??

• ????????
• Lagrange ??
• ????????
• ????? Optimal Operation Point