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MIE376 Lec 7 -Stochastic LP.page2

# MIE376 Lec 7 -Stochastic LP.page2 - MIE376 Mathematical...

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Unformatted text preview: MIE376 Mathematical Programming Lecture Notes Discrete distributions of highly correlated problem parameters In this section we assume that 0 There is a 1/3 probability that crops will be as expected 0 There is a 1/3 probability that ALL crops will be 20% higher than expected 0 There is a 1/3 probability that ALL crops will be 20% lower than expected. In order to get a handle on the incremental value of Stochastic Programming we will also solve the problem without SP, using a common sense approach. This also gives us an opportunity to ﬁrst develop the simpler deterministic LP. Simpler approach Here we 0 Formulate the LP assuming expected yields 0 Solve the LP to determine the acreages 0 Evaluate the proﬁt for each scenario 0 Calculate the expected proﬁt Let aw, ac and ab be the number of acres of wheat, corn and beets to be planted, respectively Let pW and p0 be the tons of wheat and corn to be purchased, respectively Let sw, sc, seb, and scb be the tons of wheat, corn, beets @ 36\$fI‘, and beets @10\$/ton respectively to be sold. Then using the expected yields the problem of minimizing costs can be formulated as follows Min 150 aW +230 ac +260 ab (planting cost) + 238 pW + 210 pc (purchase cost) — 170 sW — 150 sc — 36 seb — 10 scb (sales revenue) Subject to all a, p, s 20 2.5 aW + pW — SW 2 200 (wheat balance) 3 a0 + pc — sc 2 240 (corn balance) 20 ab — seb — sch Z 0 and seb S 6000 (beets balance) aW + a0 + ab 5 500 (land balance) Daniel Frances © 2011 ...
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