In this chapter we begin with a brief explanation of linear programming (LP) since integer programming (IP) is usually regarded as an extension of LP. Also most practical methods of solving IP models rely on solving an LP model first. However, our discussion of LP will be brief since this is not the main theme of this book. Although LP models are often solved in the course of solving IP models we will, in the main, regard a method of solving LP models in this context as a ‘black box’. However, we will give a (computationally inefficient) method of solving LP models which illustrates the use of the predicate calculus as discussed in Sect. 1.5 as well as demonstrating important properties of LP models which are relevant to IP. In Sect. 2.4 we discuss the comparative computational complexity of IP comparedwith LP. A list of references to the further study of LP is given in Sect. 2.5.
KeywordsConvex Hull Integer Programming Feasible Region Travel Salesman Problem Knapsack Problem
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