Omis 5120 Solutions Assignment 1

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OMIS5120 – Introduction to Quantitative Methods Solutions to Individual Assignment Question 1 [pic] Optimal Strategy: Prepare proposal and submit bid. If they win, choose excavation and new process, with an Expected Monetary Value of $142000. Question 2 [pic] Optimal Strategy: Settle out of court, with an Expected Monetary Value of $600,000. Question 3 a) Standard Model Deluxe Model Production Production Prob Demand 6000 8000 Prob Demand 2000 4000 0.3 6000 300K 250K 0.2 6000 150K 150K 0.7 8000 300K 400K 0.8 8000 150K 300K EMV 300K 355K EMV 150K 250K b) For the current solution, we have the following equation ( $355,000 = 0.3 * $250,000 + 0.7 * $400,000 ( 355K = p * 250K + (1-p) * 400K ( 355 = 250p + 400 – 400p For what value of p will the optimal solution vary (from 355K to 300K) ( 300 = 250p + 400 – 400p ( 300 – 400 = 250p – 400p ( -100 = -150p ( p = 100/150 = 2/3 or 0.67 Consequently, For p < 0.67, the optimal solution is to order 8000 For p >= 0.67, the optimal solution is to order 6000 c) Now, total production capacity is limited and, so, production levels cannot be determined independently ( See next page for decision tree and analysis Question 4 a) Conditional Costs (, $K) Event Action No Stockpile Small Stockpile Large Stockpile No Strike 0 20 50 Partial Strike 50 20 50 Total Strike 200 120 (100+20) 50* b) Weighted Costs (, $K) Prob Event Action No Stock Small Stock Large Stock 0.6 No Strike 0 12 30 0.3 Partial Strike 15 6 15 0.1 Total Strike 20

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