HW3_Solutions - IE:3610 Stochastic Modeling(Fall 2015...

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IE:3610 Stochastic Modeling (Fall 2015) Homework 3 Solutions HW3 (due Thu, Sep 17): 16.2-3(a,b,c,d, minimax regret,Hurwicz); 16.2- 6 (a,b,c, minimax regret, Hurwicz); 16.2-7 (a,b,maximin, max likelihood, minimax regret, Hurwicz); 16.2-8. Note: Use alpha=0.5 in the Hurwicz cri- terion. Additionally, find the EVPI in each of the problems 16.2-3, 16.2-6, 16.2-7, 16.2-8. 16.2-3(a,b,c, minimax regret, Hurwicz, EVPI) Solution: a) Table 1: 16.2-3 payoff table Sell 12 Sell 13 Sell 14 Sell 15 Order 12 132 132 132 132 Order 13 125 143 143 143 Order 14 118 136 154 154 Order 15 111 129 147 165 Prior Prob 0.1 0.3 0.4 0.2 b) According to the maximin criterion, Jean should purchase 12 cases Table 2: 16.2-3 maximum payoff criterion Sell 12 Sell 13 Sell 14 Sell 15 worst case payoff Order 12 132 132 132 132 132 Order 13 125 143 143 143 125 Order 14 118 136 154 154 118 Order 15 111 129 147 165 111 c) She will be able to sell 14 cases with highest probability and the maximum possible profit from selling 14 cases is earned when she buys 14 cases. Hence, according to the maximum likelihood criterion, Jean should purchase 14 cases.
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