A New Approach Based on the Learning Effect for Sequence-Dependent Parallel Machine Scheduling Problem under Uncertainty

Abstract

Production system design has lots of restrictions and complex assumptions that cause difficulty in decision making. One of the most important of them is the complexity of the relationship between man and machine. In this regard, operator learning is recognized as an effective element in completing tasks in the production system. In this research, a mathematical model for scheduling the parallel machines in terms of job degradation and operator learning is presented. As one of the most important assumptions, the sequence-dependent setup time is of concern. In other words, jobs are processed sequentially, and there is a sequence-dependent setup time. Moreover, the processing time and delivery due date are considered uncertain, and a fuzzy conversion method is used to deal with this uncertainty. The proposed mathematical model is a multiobjective one and tries to minimize speed and completion time. In order to optimize this mathematical model, the genetic algorithm (GA) and variable neighborhood search (VNS) algorithms have been used. A new hybrid algorithm has also been developed for this problem. The results show that the hybrid algorithm can provide more substantial results than classical algorithms. Moreover, it is revealed that a large percentage of Pareto solutions in the proposed algorithm have a generation time of more than 80% of the algorithm’s execution time.