A reactive approach for flexible job shop scheduling problem with tardiness penalty under uncertainty

Document Type : Article


1 Industrial Engineering Department, Faculty of Engineering, Islamic Azad University-North Tehran Branch,Tehran, Iran

2 Department of Industrial Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran

3 School of Strategy and Leadership, Faculty of Business and Law, Coventry University, Coventry, UK

4 Industrial Engineering Department, Faculty of Engineering, Islamic Azad University-North Tehran Branch, Tehran, Iran

5 Industrial Engineering and Management Department, Shahrood University of Technology, Shahrood, Iran


Flexible job shop scheduling under uncertainty plays an important role in real-world manufacturing systems. This paper deals with the flexible job shop scheduling problem to minimize the sum of jobs’ tardiness considering machines breakdown and order due date modification as two important disruptions in this production system. To this end, the problem is formulated as a mixed-integer linear programming model. In addition, two different strategies are proposed including allocating multiple machines to each job and selecting the best alternative process from other jobs to handle these disruptions. Since the problem is well-known strongly NP-hard, a hybrid metaheuristic algorithm based on the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) is proposed to solve the real-sized instances of these problems. Numerical experiments are used to evaluate the performance and effectiveness of the proposed hybrid algorithm. Obtained results for the small-sized instances show that the proposed algorithm provides proper solutions in terms of optimality and CPU Time. In addition, results for the medium- and large-sized scales validate the efficiency of the proposed algorithm and indicate that the proposed hybrid solution approach outperformed the classic GA in terms of the objective function value and the CPU time.


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