Directed perturbation analysis of an integer program

In this paper, we examine the largest tolerance levels in integer programming (IP) problems when the perturbation occurs on the right hand sides of the constraints in positive or negative directions. Based on the properties of defined stepsizes, we have not only revealed the nested and the inverted nested structures of a parametric IP with a developed algorithm, but also analyzed the configuration of a non-parametric IP with a comparative study. The complexity analysis is incorporated with numerical examples.