Many real-world problems could be modeled as linear programs except that some or all of the variables are constrained to be integers. Such problems are called integer programming problems. One might think that these problems wouldn’t be much harder than linear programming problems. For example, we saw in Chapter 13 that for network flow problems with integer data, the simplex method automatically produces integer solutions. But that was just luck. In general, one can’t expect to get integer solutions; in fact, as we shall see in this chapter, integer programming problems turn out to be generally much harder to crack than linear ones.
KeywordsInteger Programming Linear Programming Problem Feasible Region Travel Salesman Problem Piecewise Linear Function
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- Standard references for integer programming include the classic text by Garfinkel & Nemhauser (1972) and the more recent text by Nemhauser & Wolsey (1988).Google Scholar