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 for 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-sized 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. Also, the computational study confirms the proper quality of the results of the GA and VDO algorithms in medium and large-sized problems.

Keywords

• Dual-resource constrained
• flexible job-shop scheduling
• genetic algorithm
• machine breakdown
• robust fuzzy-stochastic programming
• uncertainty