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# ilp - OR 3300/5300 Optimization I Professor Bland Fall 2011...

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OR 3300/5300 Optimization I Fall 2011 Professor Bland Integer Linear Programming (BHM Ch. 9, Sections 1, 3, 4, 5, 8 has more detail on the material in this handout, however, you will not be responsible for this material on the final exam. If you take 3310/5310 in the spring, you will study this material in depth.) See the zip file of figures that accompanies this handout. 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.

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ilp - OR 3300/5300 Optimization I Professor Bland Fall 2011...

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