Robust Fuzzy-Stochastic Programming Model and Meta-Heuristic Algorithms for Dual-Resource Constrained Flexible Job-Shop Scheduling Problem Under Machine Breakdown

Abstract

Resource scheduling, job sequencing, and assigning them to available resources are the most critical issues in manufacturing systems, such as flexible job-shop systems. In addition, scheduling uncertainties have attracted significant attention in this field. This study investigates the dual-resource constrained flexible job-shop scheduling (DRCFJSS) problem under machine breakdown and operational uncertainty. Stochastic scenario-based methods were utilized to study the uncertain nature of the problem. Because process times have inherent uncertainty, they are considered fuzzy numbers and are controlled by a credibility-based measure. Robust scheduling must be developed to address unexpected disruptions, such as machine breakdowns and operational risks, such as uncertain process times. Accordingly, a novel robust fuzzy stochastic programming (RFSP) model is presented to solve this problem. In the proposed RFSP model, the objective function is formulated using a hybrid measure (i.e., a combined average-case and worst-case performance of the manufacturing system) under probable machine breakdown scenarios. Because the DRCFJSS problem is NP-hard, two types of meta-heuristic algorithms, evolutionary population-based, genetic algorithm (GA), and vibration damping optimization (VDO) algorithm, are used for large-size problems. Then, the proposed RFSP model was applied to a case study, and numerical experiments with randomly generated test problems were used. In small-sized problems, the proposed model is solved using the CPLEX solver, GA, and VDO algorithms. Computational studies indicate a higher performance of the GA compared with the other algorithms in terms of the objective function.