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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Purpose Two-stage production systems including a processing shop and an assembly stage are widely used in various manufacturing industries. These two stages are usually studied independently which may not lead to ideal results. This paper aims to deal with a two-stage production system including a job shop and an assembly stage. Design/methodology/approach Some exact methods are proposed based on branch and bound (B&B) approach to minimize the total completion time of products. As B&B approaches are usually time-consuming, three efficient lower bounds are developed for the problem and variable neighborhood search is used to provide proper upper bound of the solution in each branch. In addition, to create branches and search new nodes, two strategies are applied including the best-first search and the depth-first search (DFS). Another feature of the proposed algorithms is that the search space is reduced by releasing the precedence constraint. In this case, the problem becomes equivalent to a parallel machine scheduling problem, and the redundant branches that do not consider the precedence constraint are removed. Therefore, the number of nodes and computational time are significantly reduced without eliminating the optimal solution. Findings Some numerical examples are used to evaluate the performance of the proposed methods. Comparison result to mathematical model (mixed-integer linear programming) validates the performance accuracy and efficiency of the proposed methods. In addition, computational results indicate the superiority of the DFS strategy with regard to CPU time. Originality/value Studies about the scheduling problems for two-stage production systems including job shop followed by an assembly stage traditionally present approximate method and metaheuristic algorithms to solve the problem. This is the first study that introduces exact methods based on (B&B) approach.

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