Abstract This study addresses the optimization of production planning and scheduling for human–robot interaction in a fuzzy environment, a critical challenge in modern manufacturing, especially under fluctuating market demand. The proposed model simultaneously determines production quantities, inventory/shortage levels, human–robot task allocation, and job sequencing. All decisions are optimized in a multi-period, multi-product setting. Three objective functions are considered: maximizing net present value, minimizing maximum completion time, and minimizing total early and tardy times. To handle uncertainties in demand and processing times, a pessimistic (credibility-constrained) fuzzy programming approach is employed. The model is solved using the epsilon-constraint method for small-scale problems and metaheuristic algorithms (NSGA-II, MOPSO, and MOWOA) for larger instances. Sensitivity analyses reveal that reducing completion times increases costs, lowering net present value, while higher uncertainty rates increase production times and shortages, reducing net present value. A 4% increase in bank interest rate reduces net present value by 15.68%, with no impact on completion or early/tardy times. The MOWOA algorithm demonstrates superior performance in generating efficient solutions for large-scale problems, offering practical insights for optimizing human–robot collaboration in manufacturing.
Deng et al. (Fri,) studied this question.