A novel bi-objective model for a job shop scheduling problem with consideration of Fuzzy parameters, modified learning effects and multiple preventive maintenance activities

Document Type : Article


1 Industrial engineering Department, University of Kurdistan, Sanandaj,Iran

2 Department of industrial engineering, University of Kurdistan, Pasdaran Boulevard, Sanandaj, Iran

3 Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran


This paper aims at introducing a novel bi-objective model for a Job Shop Scheduling Problem (JSSP) in order to minimize makespan and maximum tardiness simultaneously. Some realistic assumptions, i.e. Fuzzy processing times and due dates involving triangular possibility distributions, transportation times, availability constraints, modified position-based learning effects on processing times, and sum-of-processing-time based learning effects on duration of maintenance activities have been considered, to provide a more general and practical model for the JSSP. Based on the learning effects, Processing times decrease as a machine performs an operation frequently, and workers gain working skills and experiences. In this paper based on DeJong’s learning effect a novel and modified formulation has been proposed for this effect. According to the above-mentioned assumptions, a novel mixed-integer linear programming (MILP) model for the JSSP is suggested. The proposed model is first converted to an auxiliary crisp model, given that model is a possibilistic programming, it is then solved by the TH and ε-constraint methods for small instances, and the results are compared. For medium and large instances, five metaheuristic algorithms, including NSGA-ΙΙΙ, PESA-ΙΙ, SPEA-ΙΙ, NSGA-ΙΙ, and MOEA/D are utilized, and the results are finally compared on the basis of three performance metrics.