Module10 Handouts Integer LP

Module10 Handouts Integer LP - _0,1logicaltype...

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8/20/2010 1 Integer Programming IPM or ILPM Like LPMs but with added constraint that some or all of the decision variables are integers. Also includes binary or {0,1} logical type decision variables The integer requirement adds a constraint so the objective function value for IPM cannot be better than that of the corresponding LPM without the integer constraint Objective and constraint expressions are still linear Learning Objectives Integer Linear Programming Integer Linear Programming Models (IPMs) Types of IPMs Graphical solutions for all integer models Computer solution for all types of IPM Decision applications using all {0,1} D.V.s Modeling flexibility using {0,1} D.V.s
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8/20/2010 2 Integer Programming Models Advantages: More realistic More model flexibility Disadvantages Can be much more difficult to solve More difficult to formulate Lack of sensitivity analysis LP Relaxation of IP Model Same model but without the integer constraint Solution to LP relaxation of IP Upper bound for a MAX objective Lower bound for a MIN objective If you solve LPM and get all integers for optimal solution of decision variables you know optimal solution for the corresponding IP. When can you round the optimal solution to the relaxation LP and have a good approximate optimal solution to the IP problem?
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Module10 Handouts Integer LP - _0,1logicaltype...

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