Revue d'économie et de statistique appliquée
Volume 20, Numéro 1, Pages 140-148
2023-06-01
A Model For Generalized Assignement Problem. Bilinear Case (bgap) Local And Global Approach
Authors : Layouni Zoubir . Muhammad Suhail .
Abstract
Despite recent increases in automation of production systems, the human factor has emerged as one of the most important aspects of a company's competitiveness in this changing environment. This evolution of the industrial world has involved a perpetual questioning of the production methods and in particular the methods of taking into account the operators. The rational use of human resources during the organization of activities becomes one of the concerns of companies. Aware of this fact, several researchers have taken an interest in the management of human resources and in particular in the problem of assignment. Behind this problem, there is actually a set of problems that vary according to the objective of optimization, constraints taken into account. We are going to expose a solution for generalized assignment problem with bilinear form, it consist to minimize the cost of the assignments subjects to a set of specific constraints. The problem of bilinear programming was introduced by Konno [1]. Several practical cases can be modelled under this special form. We proposed two successive approaches to solving the problem based on the equivalence between bilinear program and concave minimization using two distinct polyhedrons and the formal linearity of a dual problem formulation.
Keywords
Generalized Assignment Problem ; Bilinear Program ; Global and local search ; Optimization
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