ABSTRACT
Chapter 7 introduces the important topic of integer linear programming (ILP), which provides (i) qualitative improvements due to more realistic solutions, namely when decision variables require integer values; and (ii) better modeling capabilities, for example, with binary variables formulating contingency decisions or fixed charge costs. However, such qualitative improvements come at a cost to quantitative reductions: the LP optimal value is the hard limit for the branch-and-bound (B&B) method, considering also that the solutions space is successively reduced and the objective value is successively cut. In the opposite sense to the generalization approach, B&B follows a reduction approach that quantitatively constrains the objective function; however, both the modeling features and the integrity attributes largely enhance decision-making through ILP.
