Three Hybrid Metaheuristic Algorithms for Stochastic Flexible Flow Shop Scheduling Problem with Preventive Maintenance and Budget Constraint

Document Type: Original Manuscript


School of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran



Stochastic flexible flow shop scheduling problem (SFFSSP) is one the main focus of researchers due to the complexity arises from inherent uncertainties and also the difficulty of solving such NP-hard problems. Conventionally, in such problems each machine’s job process time may encounter uncertainty due to their relevant random behaviour. In order to examine such problems more realistically, fixed interval preventive maintenance (PM) and budget constraint are considered.PM activity is a crucial task to reduce the production efficiency. In the current research we focused on a scheduling problem which a job is processed at the upstream stage and all the downstream machines get busy or alternatively PM cost is significant, consequently the job waits inside the buffers and increases the associated holding cost. This paper proposes a new more realistic mathematical model which considers both the PM and holding cost of jobs inside the buffers in the stochastic flexible flow shop scheduling problem. The holding cost is controlled in the model via the budget constraint. In order to solve the proposedmodel, three hybrid metaheuristic algorithms are introduced. They include a couple of well-known metaheuristic algorithms which have efficient quality solutions in the literature. The two algorithms of them constructed byincorporationof the particle swarm optimization algorithm (PSO) and parallel simulated annealing (PSA) methods under different random generation policies. The third one enriched based on genetic algorithm (GA) with PSA. To evaluate the performance of the proposed algorithms, different numerical examples are presented. Computational experiments revealed that the proposed algorithms embedboth desirable accuracy and CPU time. Among them, the PSO-PSAП outperforms than other algorithms in terms of makespan and CPU time especially for large size problems.

Graphical Abstract

Three Hybrid Metaheuristic Algorithms for Stochastic Flexible Flow Shop Scheduling Problem with Preventive Maintenance and Budget Constraint


  • An optimization model for stochastic flexible flow shop scheduling problems presented
  • The proposed method covers uncertainties arise due random process time, preventive maintenance activities and budget constraint.
  • Two metaheuristic algorithms constructed byincorporation of PSO and PSA methods under different random generation policies.
  • Furthermore a metaheuristic algorithms based on GA and PSA presented.
  • Performance of the proposed algorithms compared by different numerical examples.


Main Subjects

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