The recently defined class of integer programming games (IPG) models situations where multiple self-interested decision makers interact, with their strategy sets represented by a finite set linear constraints together requirements. Many real-world problems can suitably be fit in this class, and hence anticipating IPG outcomes is crucial value for policy regulators. Nash equilibria have been wid...

A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of $$n \Delta $$ on the proximity optimal solutions Integer Linear Programming problem its standard linear relaxation. In this bound, n is number variables $$\Delta denotes maximum absolute values subdeterminants constraint matrix. Hochbaum Shanthikumar, Werman Magagnosc showed that same valid if a more general co...

This paper develops an integer programming approach to two‐sided many‐to‐one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that exists in discrete when the firms' preference profile satisfies total unimodularity condition compatible with various forms complementarities. provide class profiles satisfy this condition.

This paper considers the Tchebychev distance for a facility location problem with a probabilistic line barrier in the plane. In particular, we develop a mixed-integer nonlinear programming (MINLP) model for this problem that minimizes the total Tchebychev distance between a new facility and the existing facilities. A numerical example is solved to show the validity of the developed model. Becau...

In recent years, Supplier evaluation and selection, an important element in supply chain management, has been gaining attention in both academic literature and industrial practice. The Mixed integer multi-Objective non-Linear programming model (MIMONLP) presented in this paper aimed to evaluate and select the appropriate set of suppliers considering quantitative and qualitative criteria and in ...