Mixed Integer Linear Programming Models for Combinatorial Optimization Problems

• Published in: Concepts of Combinatorial Optimization pp. 101 - 133
• Main Author: Della Croce, Frédérico
• Format: Book Chapter
• Language: English
• Published: Hoboken, NJ, USA John Wiley & Sons, Inc 10.07.2014
• Subjects: combinatorial optimization problems; general modeling techniques; integer linear programming; mixed integer linear programming (MILP)
• ISBN: 1848216564; 9781848216563
• DOI: 10.1002/9781119005216.ch5

This chapter provides an insight into mixed integer linear programming (MILP) modeling of combinatorial optimization problems. First, introductory MILP models are recalled together with general modeling techniques; then more or less standard MILP formulations of several combinatorial optimization problems are discussed. The chapter focuses on several modeling tricks that enable generation of linear models in the presence of special types of non‐linear expressions or in the presence of logic conditions between real/integer variables and/or between binary variables. Typically, a MILP model is considered “good” if its continuous linear programming relaxation is sufficiently tight, that is the optimal solution value of the continuous linear programming relaxation is sufficiently close to the optimal solution value of the considered problem.