Multiple cost coefficients sensitivity theorems of integer linear optimization

Abstract

In practical integer optimization applications, perturbations of multiple cost coefficients often occur simultaneously. One important example is the perturbation of the probability distribution estimates for scenarios of a stochastic integer optimization cost function formulation. This study aims to develop multiple cost coefficients sensitivity theorems, which indicate that the optimal solution remains the same if the perturbation amount of cost coefficients is greater than or equal to the derived bounds. We developed two sensitivity theorems. One depends on the underlying algorithm, the iterative dual method proposed by Bell and Shapiro , and the other directly uses the optimal integer output that can be obtained by any algorithms. We carried out numerical experiments using the two proposed theorems separately to compare their effectiveness and computational tractability. These theorems are useful especially when dealing with the problems where the cost coefficients change frequently.