Dual resource constrained flexible job shop scheduling with sequence-dependent setup time

This study addresses the imperative need for efficient solutions in the context of the dual resource constrained flexible job shop scheduling problem with sequence-dependent setup times (DRCFJS-SDSTs). We introduce a pioneering tri-objective mixed-integer linear mathematical model tailored to this complex challenge. Our model is designed to optimize the assignment of operations to candidate multi-skilled machines and operators, with the primary goals of minimizing operators' idleness cost and sequence-dependent setup time-related expenses. Additionally, it aims to mitigate total tardiness and earliness penalties while regulating maximum machine workload. Given the NP-hard nature of the proposed DRCFJS-SDST, we employ the epsilon constraint method to derive exact optimal solutions for small-scale problems. For larger instances, we develop a modified variant of the multi-objective invasive weed optimization (MOIWO) algorithm, enhanced by a fuzzy sorting algorithm for competitive exclusion. In the absence of established benchmarks in the literature, we validate our solutions against those generated by multi-objective particle swarm optimization (MOPSO) and non-dominated sorted genetic algorithm (NSGA-II). Through comparative analysis, we demonstrate the superior performance of MOIWO. Specifically, when compared with NSGA-II, MOIWO achieves success rates of 90.83% and shows similar performance in 4.17% of cases. Moreover, compared with MOPSO, MOIWO achieves success rates of 84.17% and exhibits similar performance in 9.17% of cases. These findings contribute significantly to the advancement of scheduling optimization methodologies.