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Integer Optimization

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Basic Concepts Integer Linear Program(ILP): A linear program except that some or all of the decision variables must have integer values. LP Relaxation: A LP model that is derived from an ILP by dropping the integer requirements for the variables. –In a Max model, the OV of the LP relaxation always provides an upper bound on the OV of ILP –In a Min model, the OV of the LP relaxation always provides a lower bound on the OV of ILP

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Why not just use rounded solution of LP? Rounded solution may be infeasible. Even if one or more of the neighboring integer points is feasible: –Such a point need not be optimal for the ILP. –Such a point need not even be near the optimal ILP solution. (see figure 6.4 on p.293 of the text)

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Types of Integer Program All-Integer Linear Program: All of the decision variables are required to be integer. Mixed Integer Linear Program(MILP): Some, but not all, of the decision variables in a LP are required to be integer. Binary (0-1 )Integer Linear Program: The integer variables are only permitted to assume the values zero or one. It may be of either the all-integer or MILP type.

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(Not in text). An LP with additional constraints requiring that all the variables be integers is called an all-integer linear program (IP). The LP.

(Not in text). An LP with additional constraints requiring that all the variables be integers is called an all-integer linear program (IP). The LP.

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