stochprog_computing.pdf - Lecture notes for Stochastic...

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Lecture notes for Stochastic Programming: CO370, fall 2017 Ricardo Fukasawa Consider the newsvendor problem: A newsvendor needs to buy newspapers at the beginning of the day. He buys at a price of $0.2 per newspaper. During the day, he sells newspapers at $1 per newspaper. At the end of the day, any unsold newspapers he can sell to recycle at $0.10 per newspaper. How many newspapers should the newsvendor buy to maximize profit? There are three demand scenarios 1. Scenario with probability 0.25, demand is 40 2. Scenario with probability 0.5, demand is 60 3. Scenario with probability 0.25, demand is 20 The two stage model is as follows: First stage decision variable: x represents how many newspapers to buy at the beginning of the day Second stage decision variables: y s represent how many newspapers to sell at $1 and w s represents how many newspapers to sell at $0.1 in scenario s , for s = 1 , 2 . 3. The two stage model will then be: max - 0 . 2 x + 3 s =1 p s ( y s + 0 . 1 w s ) s.t. x 0 y s d s , s = 1 , . . . , 3 y s + w s x, s = 1 , . . . , 3 y, w 0 (1)
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