Optimizing the Problem of Production Planning and Human-Robot Communication Scheduling in Fuzzy Conditions

Introduction: Production planning, scheduling, and sequencing form the core functions of manufacturing companies. The evolving and fluctuating market demands have turned production into a challenge, as companies must deliver high-quality products using minimal resources while responding to uncertain market demands. Therefore, the need for efficient production planning, scheduling, and sequencing has become a crucial research area for both companies and researchers in recent decades. This paper addresses the modeling and solution of a production planning and scheduling problem related to human-robot collaboration under fuzzy conditions. The proposed model aims to determine optimal decisions such as production quantity, human-robot allocation for product manufacturing on each line, processing time, and product production scheduling. To achieve integrated decisions for production planning and scheduling in human-robot collaboration, three objective functions are considered: maximizing the net present value, minimizing the maximum completion time of product manufacturing, and minimizing the total early and tardy times.
Methods: Since demand quantity and processing time are considered uncertain parameters in this problem, a pessimistic fuzzy programming approach is used to handle these parameters. To solve the three-objective model, the epsilon-constraint method, the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-objective Particle Swarm Optimization (MOPSO), and Multi-objective Whale Optimization Algorithm (MOWOA) are applied. Thus, for solving the problem in small sizes and performing sensitivity analysis of the mathematical model, the epsilon-constraint method is used, while for solving larger-sized problems, metaheuristic algorithms are employed.
Results and Discussion: The analysis of the mathematical model under uncertainty reveals that reducing the maximum completion time of product manufacturing decreases both the net present value and the total early and tardy times. Controlling the model using fuzzy programming and the uncertainty rate also shows that increasing this parameter leads to a reduction in net present value and an increase in the maximum completion time of product manufacturing. Furthermore, analyzing various numerical examples of different sizes indicates that the solution quality of the MOWOA, NSGA-II, and MOPSO algorithms is superior to that of the epsilon-constraint method. Among these algorithms, MOWOA achieves the highest number of efficient solutions with the smallest branch distance metric and the shortest distance from the ideal point.
Conclusion: The analyses indicate that the highest total early and tardy times occur when the uncertainty rate is set at 0.5. Additionally, sensitivity analysis of the bank interest rate shows that a 4% increase in the interest rate results in a 15.68% reduction in the net present value. The bank interest rate has no impact on the maximum completion time of product manufacturing or the total early and tardy times. The analysis of numerical examples with various sizes also demonstrates that the epsilon-constraint method is incapable of solving larger numerical examples, and the quality of the results obtained from metaheuristic algorithms is superior to that of the exact method. Moreover, the number of efficient solutions, the widest spread, and the solution time are better in the metaheuristic algorithms than in the epsilon-constraint method. Among the metaheuristic algorithms, MOWOA exhibits superior performance compared to other solution methods.