# lect19 - ISE 536Fall03 Linear Programming and Extensions...

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November 12, 2003 Lecture 19: Bender’s Decomposition Lecturer: Fernando Ord´o˜nez 1 Motivation: Stochastic Programming An electric utility company faces the problem of satisfying demand at minimum cost. In the case of a thermal plant and a hydro plant, satisfying the demand over the next two periods can be written as: min 3 x 1 + 3 x 2 x 1 + h 1 10 x 2 + h 2 12 h 1 5 h 2 V 2 V 2 + h 1 = 5 + r x i , h i 0 Note that this is a production and inventory problem. Suppose - 2nd period demand can be 15 or 10 each with prob. 1/2 - 2nd period thermal cost can be 1 or 5 each with prob. 1/2 - rain can be r = 0 or r = 10 each with prob. 1/2 Question: What is the best strategy to satisfy 1st period demand taking into account this uncertainty? scenario prob. 2nd demand thermal cost rain best strategy 1 0.125 15 5 0 save water, x 1 high 2 0.125 10 3 10 use water, x 1 low . . . . . . 1

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lect19 - ISE 536Fall03 Linear Programming and Extensions...

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