عنوان مقاله [English]
In this paper, a flexible job shop scheduling problem (FJSP) with assembly operations and sequence dependent setup time is studied. In this problem, each product is produced from assembling a set of several different parts. At first, the parts are processed in a flexible job shop system. Setup time is needed when a machine starts processing the parts or it changes items. Then in the second stage, the parts are assembled and products are produced. The assembly operation cannot be started for a product until the set of parts are completed in machining operations. In this paper, we presented a mathematical model for a flexible job shop scheduling problem with assembly operations and sequence dependent setup time. The objective is to minimize the completion time of all products (makespan). Since the problem is NP-hard, one particle swarm optimization (PSO) algorithm and two hybrid metaheuristic algorithms based on particle swarm optimization are proposed. The proposed hybrid algorithms are called, respectively, hybrid particle swarm optimization with a variable neighborhood search algorithm (HPSOVNS) and hybrid particle swarm optimization with a simulated annealing algorithm (HPSOSA). In these hybrid algorithms, we used particle swarm optimization (PSO) algorithm for global exploration at search space and variable neighborhood search (VNS)/ simulated annealing (SA) algorithm for local search at around solutions obtained in the each iteration.
In order to evaluate and validate the performance of the proposed algorithms, we are designed numerical experiments and results are compared with hybrid genetic algorithm and tabu search (HGATS) presented by Li and Gao. For this purpose, the proposed mathematical model is coded in GAMS software and the proposed metaheuristic algorithms are coded in MATLAB software. For obtaining better and more sustainable results of the metaheuristic algorithms, Minitab software was used to design the experiments and assign the best level to the size of problems. For the problems in the small size, the optimal solution is obtained by GAMS software. Then a randomized complete block design considered to compare the ability of algorithms at finding the best solution for medium and large problems. Computational results revealed that for medium and large problems the HPSOVNS algorithm outperforms the HPSOSA, PSO and HGATS algorithms.