Integer and Mixed Integer Linear Fractional Programming

Abstract

Some of the problems mentioned in Chapter 1 required that either part of the variables, or all of them take integer values. This chapter will study such problems. In particular, we will address the bivalent programming in which part of the variables or all of them can take only values 0 or 1 (Section 9.1). Distinction will be made between integer fractional programming where all the variables must be integers, and mixed integer fractional programming, where only part of the variables need be integers. To solve these problems we will try to adapt some of the methods presented in Chapter 3 for fractional programming with continuous variables, e.g., methods based on the Simplex algorithm, parametric methods, and the method of the change of variable. Additionally, we will also present branch and bound methods, and methods using the cutting planes.