# hw1 - IE 495 Stochastic Programming Problem Set#1 Due Date...

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IE 495 – Stochastic Programming Problem Set #1 Due Date: February 3, 2003 Do any four of the following ﬁve problems. If you are working in pairs, do all ﬁve problems. You are allowed to examine outside sources, but you must cite any references that you use. Please don’t discuss the problems with other members of the class (other than your partner, if you are working with one). 1 Random Linear Programs and the Distri- bution Problem Recall the random linear program that we saw in class: minimize x 1 + x 2 subject to ω 1 x 1 + x 2 7 ω 2 x 1 + x 2 4 x 1 0 x 2 0 with ω 1 ∼ U [1 , 4] and ω 2 ∼ U [1 / 3 , 1]. Let ( x * 1 ( ω ) ,x * 2 ( ω )) be the optimal solution for a given value of ω = ( ω 1 2 ). v * ( ω ) = x * 1 ( ω ) + x * 2 ( ω ) be the optimal objective function value. 1.1 Problem Calculate x * 1 ( ω ) ,x * 2 ( ω ) , and v * ( ω ) for all ω Ω = [1 , 4] × [1 / 3 , 1]. 1.2 Problem

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hw1 - IE 495 Stochastic Programming Problem Set#1 Due Date...

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