A Mathematical Model for Double Resource Constraint Flexible Job-shop Scheduling Problem Considering the Limit of Preventive Maintenance

Abstract

In the field of scheduling and sequence of operations, one of the common assumptions is the availability of machines and workers on the planning horizon. In the real world, a machine may be temporarily unavailable for a variety of reasons, including maintenance activities, and the full capacity of human resources cannot be used due to their limited number and/or different skill levels. Therefore, this paper examines the Dual Resource Constrained Flexible Job Shop Scheduling Problem (DRCFJSP) considering the limit of preventive maintenance (PM). Due to various variables and constraints, the goal is to minimize the maximum completion time. In this regard, Mixed Integer Linear Programming (MILP) model is presented for the mentioned problem. To evaluate and validate the presented mathematical model, several small and medium-sized problems are randomly generated and solved using CPLEX solver in GAMS software. Because the solving of this problem on a large scale is complex and time-consuming, two metaheuristic algorithms called Genetic Algorithm (GA) and Vibration Damping Optimization Algorithm (VDO) are used. The computational results show that GAMS software can solve small problems in an acceptable time and achieve an accurate answer, and also meta-heuristic algorithms can reach appropriate answers. The efficiency of the two proposed algorithms is also compared in terms of computational time and the value obtained for the objective function.

Keywords

• flexible job-shop scheduling
• dual resource constraint
• preventive maintenance
• genetic algorithm
• vibration damping optimization algorithm.