# Lab 6 - UniversityofToronto...

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University of Toronto Department of Mechanical and Industrial Engineering MIE376: Mathematical Programming Winter 2011 Lab 6 – Column Generation 1. Cutting Stock Problem Using the Cutting Stock Problem from class: Suppose we the material comes in 107m lengths and we need 25 3m boards, 20 5m boards and 15 9m boards. How many units of the original material do we need? Formulating the problem as a column generation problem, we can solve the problem in AMPL. Master Problem : Choosing with of the feasible Cuts to meet the demand (starting with an initial feasible cut) Let x i be a how many cuts of cut i to make from the raw material, an integer value Let a ij be how many boards of size j to cut from the 107m material in cut i min ෍ ݔ ݏݑܾ݆݁ܿݐ ݐ݋: ෍ ܽ ௜௝ ݔ ௜௝ ൒ݎ݁ݍ SubProblem : Finding a new feasible Cut max ܿ ܤ ିଵ ܽ ௡௘௪,௝ െ1 ݏݑܾ݆݁ܿݐ ݐ݋: ෍ ܽ ௡௘௪,௝ ݈݁݊݃ݐ݄ ൑ 107 ܽ ௡௘௪,௝ ൒0 ,integer

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## This note was uploaded on 04/20/2011 for the course MIE 376 taught by Professor Daniel during the Spring '11 term at University of Toronto.

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Lab 6 - UniversityofToronto...

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