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Unformatted text preview: IE 335 Operations Research  Optimization Solutions to Homework 12 Spring 2011 Problem 55 Let us define the decision variables for y i for i = 1 ,..., 8: y i = 1 if block i is used 0 otherwise And x ji for i,j = 1 ,..., 8 as: x ji = 1 if commercial j is assigned to block i 0 otherwise minimize 8 X i =1 y i minimize total number of blocks used subject to 15 x 1 i + 16 x 2 i + 20 x 3 i + 25 x 4 i + 30 x 5 i + 35 x 6 i + 40 x 7 i + 50 x 8 i ≤ 60 y i for i = 1 ,..., 8 60second block constraint 8 X i =1 x ji = 1 for j = 1 ,..., 8 each commercial can only be assigned to one block y i ∈ { , 1 } for i = 1 ,..., 8 x ji ∈ { , 1 } for i = 1 ,..., 8 and for j = 1 ,..., 8 Problem 56 Bertsimas&Tsitsiklis 1997 Let us define the decision variables y i for i = 1 ,...,m as: y i = 1 if box i is used 0 otherwise And x ji for i = 1 ,...,m and j = 1 ,...,n as: x ji = 1 if item j is placed in box i 0 otherwise 1 maximize 0 subject to m X i =1 b i y i ≤ Q Truck size constraint n X j =1 a j x ji ≤ y...
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This note was uploaded on 04/27/2011 for the course IE 335 taught by Professor Smith during the Spring '11 term at Southwestern.
 Spring '11
 Smith
 Operations Research, Optimization

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