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

Abstract

This paper aims to introduce a novel bi-objective model for a Job Shop Scheduling Problem (JSSP) in order to minimize makespan and maximum tardiness simultaneously. Some realistic assumptions namely 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-times based learning effects on duration of maintenance activities were considered to provide a more general and practical model for the JSSP. Based on the learning effects, processing times decrease as the machine performs an operation frequently and workers gain working skill and experience. In this paper, based on DeJong's learning effect, a novel and modified formulation is 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 into an auxiliary crisp model, given that the model is a possibilistic programming and is then solved by TH and "-constraint methods in the case of small-sized instances. Finally, the results are compared. For medium- and large-sized instances, ve metaheuristic algorithms including Non-dominated Sorting Genetic Algorithm (NSGA-III), Pareto Envelope-based Selection Algorithm (PESA-II), Strength Pareto Evolutionary Algorithm (SPEA-II), NSGA-II, and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) are utilized, and the results are finally compared in terms of three performance metrics.