ilp - OR 320/520 Optimization I 11/29/07 Professor Bland...

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Unformatted text preview: OR 320/520 Optimization I 11/29/07 Professor Bland Integer Linear Programming (see BHM Ch. 9, Sections 1, 3, 4, 5, 8) Minimize n X j =1 c j x j s . t . n X j =1 a ij x j = b i ( i = 1 , . . . , m ) (ILP) x j ≥ 0 and integer ( j = 1 , . . . , n ) . (May maximize rather than minimizing, may have ≤ , ≥ , constraints, etc. May have some variables that are required to be integer-valued, others not.) Assume a ij ’s, c j ’s b i ’s are integer-valued (or, at least rational). If we drop the integrality conditions from (ILP) we get the linear programming relaxation . (ILP) has very broad applicability: • indivisible commodities • batch-sizing and fixed charges • “go, no-go” decisions • logical constraints, conditional constraints • sequencing and precedence constraints • piecewise-linear approximation of nonlinear functions. ILP’s are typically much harder to solve than LP’s. Why? The set of feasible solutions is not convex, so it is hard to check optimality....
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This note was uploaded on 03/30/2008 for the course ORIE 320 taught by Professor Bland during the Fall '07 term at Cornell.

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ilp - OR 320/520 Optimization I 11/29/07 Professor Bland...

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