Tutorial Guide to Mixed-Integer Programming Models and Solution Techniques

TL;DR: This chapter begins by discussing basic mixed-integer programming formulation principles and tricks, especially with regards to the use of binary variables to form logical statements, and discusses two core techniques, branchand-bound and cutting-plane algorithms, used to solve mixed- integer programs.

Abstract: Mixed-integer programming theory provides a mechanism for optimizing decisions that take place in complex systems, including those encountered in biology and medicine. This chapter is intended for researchers and practitioners wanting an introduction to the field of mixed-integer programming. We begin by discussing basic mixed-integer programming formulation principles and tricks, especially with regards to the use of binary variables to form logical statements. We then discuss two core techniques, branchand-bound and cutting-plane algorithms, used to solve mixed-integer programs. We illustrate the use of mixed-integer programming in the context of several medical applications, and close with a featured study on Intensity Modulated Radiation Therapy planning.