Title: Utility Theory
1Production Information and Decision Systems Final
Presentation
Utility Theory ?????????????
????????? ???????????
2Goal?? Optimal Operation Point
Indifference Curve
Cycle Time (better gt)
Optimal Operation Point
Option Curve
Throughput (better gt)
3??????
??Option Curve????? ????Throughput? Cycle
Time?Data,???????????oc(x)
??????? ????Throghput?????Cycle Time???????W
??????????,oc(x)????,??Lagrange?????????
4? Queuing Capacity Model ?????????,????? scatter
diagram ,????????????
Cycle Time (better gt)
Throughput (better gt)
5????????????
???????,???????????????
6??????????
??
?? 1. MSE 0.053399 2. ???????????? 3.???
Option Curve ?????
Cycle Time (better gt)
Throughput (better gt)
7??????????
??
?? 1. MSE 0.011198 2.?????????????
,??????????
Cycle Time (better gt)
Throughput (better gt)
8??????????
??
?? 1. MSE 0.002379 2. ??????,?????
Cycle Time (better gt)
Throughput (better gt)
9?????????
??
?? 1.MSE 0.0099569 2.???????,?????
Cycle Time (better gt)
Throughput (better gt)
10???????
Throughput ???? UTH
Cycle Time ???? UCT
??????
????? U
11????????????
Indifference Curves
Option Curve
12Lagrange ???????
????????? U(x,y)
???? OCE(x,y) 0 OC(x) - y
Lagrange??
??????????? x, y
- ?????
- ?(x,y)???????
- ?? m ???? n ?? ??,??????
13Optimal 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
14??????????????????
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
15??
- ????????
- Lagrange ??
- ????????
- ????? Optimal Operation Point