ABSTRACT
Mathematical programming problems in which the variables are constrained to have integer values are called integer programming problems. Many engineering, industrial, and financial applications involve integer constraints. For example, in a manufacturing scenario, it would be difficult to implement a solution that specifies producing 10.4 cars or 7.2 tables. Fractional values are infeasible. For integer programming problems, the feasible region is neither continuous nor convex, as illustrated in Figure 4.1 for a simple two-dimensional integer problem. Observe that the feasible points for this problem do not lie at the extreme points of the region, or even on the boundaries; and in fact, the elegant solution techniques that have been developed for solving linear programming problems generally do not find solutions to integer problems. The Simplex method for linear programming converges to a solution at an extreme point which is typically a point, with fractional variables. Graphical representation. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315274188/0404ff86-3b42-4d8a-b206-d60e32d91ae0/content/fig4_1.tif"/>
