Purpose The purpose of this paper is to present a mathematical model and a new hybrid algorithm for flexible job shop scheduling problem with assembly operations. In this problem, each product is produced by assembling a set of several different parts. At first, the parts are processed in a flexible job shop system, and then at the second stage, the parts are assembled and products are produced. Design/methodology/approach As the problem is non-deterministic polynomial-time-hard, a new hybrid particle swarm optimization and parallel variable neighborhood search (HPSOPVNS) algorithm is proposed. In this hybrid algorithm, particle swarm optimization (PSO) algorithm is used for global exploration of search space and parallel variable neighborhood search (PVNS) algorithm for local search at vicinity of solutions obtained in each iteration. For parameter tuning of the metaheuristic algorithms, Taguchi approach is used. Also, a statistical test is proposed to compare the ability of metaheuristics at finding the best solution in the medium and large sizes. Findings Numerical experiments are used to evaluate and validate the performance and effectiveness of HPSOPVNS algorithm with hybrid particle swarm optimization with a variable neighborhood search (HPSOVNS) algorithm, PSO algorithm and hybrid genetic algorithm and Tabu search (HGATS). The computational results show that the HPSOPVNS algorithm achieves better performance than competing algorithms. Practical implications Scheduling of manufacturing parts and planning of assembly operations are two steps in production systems that have been studied independently. However, with regard to many manufacturing industries having assembly lines after manufacturing stage, it is necessary to deal with a combination of these problems that is considered in this paper. Originality/value This paper proposed a mathematical model and a new hybrid algorithm for flexible job shop scheduling problem with assembly operations.

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In this research, an integrated scheduling problem of job shop systems with an assembly stage and transportation to minimize the total tardiness time is studied. In this problem, the parts are processed in a job shop system and then assembled in the assembly stage. Ultimately, the products are shipped in packages to customers. Setup time is assumed to depend on sequence. At first, a mixed-integer linear model is developed. Since the problem is NP-hard, a hybrid imperialist competitive and simulated annealing (ICA-SA) algorithm is proposed to solve the problems with the medium and large sizes. To validate the performance of the proposed algorithm, results are compared to an imperialist competitive algorithm and a hybrid imperialist competitive and tabu search (ICA-TS) algorithm. Analysis of variance random block design is used to compare the results of the algorithms. P-values of algorithms and blocks in this test are smaller than the significance level of 0.05. The computational results show that the proposed hybrid algorithm achieves better performance than the imperialist competitive algorithm and hybrid imperialist competitive and tabu search.