A Goal Programming Model for Multi-Resource Generalized Assignment Problem that Contains Agents With Different Abilities and Priorities Along With Jobs to Be Assigned to the Same Agents

Abstract

Generalized Assignment Problem (GAP) is assignment of jobs to agents with capacity constraints. For Multi Resource GAP (MR-GAP), as an extension of GAP, each agent has a certain number of constrained resources. The aim of the problem is to minimize the total assignment cost. Here, each job is assigned to exactly one agent. In this study, a special kind of MR-GAP, consisting of agents with certain aptitudes and priorities in association with jobs that necessitate assigning to the same agent is considered. The motivation of this study is the problem confronted by a refrigerator factory, to assign the plastic injection molds to supplier firms. A mixed binary integer goal-programming model is developed for considered problem. The performance of the proposed mathematical model is tested by using instances with different characteristics. GAMS/Cplex solver is used to solve those instances. The results obtained, proved that the proposed model is capable to solve the real life problems successfully.

Keywords

• Multi-resource generalized assignment problem
• Plastic injection mold assignment problem
• Goal programming