A Gilmore-Gomory-Type Construction of Integer Programming Value Functions

Abstract

In this paper, we analyze how sequentially introducing decision variables into an integer program (IP) affects the value function and its level sets. In particular, we use a Gilmore-Gomory-type approach to construct IP value functions over a restricted set of variables. We introduce the notion of maximally-contiguous subsets of level sets -volumes in which changes to the constraint right-hand side have no effect on the value function -and relate these structures to IP value functions and optimal solutions.