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.

Optimization problems are not only formed into a linear programming but also nonlinear programming. In real life, often decision variables restricted on integer. Hence, came the nonlinear programming. One particular form of nonlinear programming is a convex quadratic programming which form the objective function is quadratic and convex and linear constraint functions. In this research designed ...

An algorithm for solving linear programming problems can be used as a subroutine in methods for more complicated problems. Such methods usually involve solving a sequence of related linear programming problems, where the solution to one linear program is close to the solution to the next, that is, it provides a warm start for the next linear program. The branch and cut method for solving intege...

this paper studies the hybrid flow shop scheduling where the optimization criterion is the minimization of total tardiness. first, the problem is formulated as a mixed integer linear programming model. then, to solve large problem sizes, an artificial immune algorithm hybridized with a simple local search in form of simulated annealing is proposed. two experiments are carried out to evaluate th...