Flexible job shop rescheduling using user preferences

Abstract

We consider solving the flexible job shop scheduling problem, where new jobs arrive and must be inserted into the production line through rescheduling. The insertion of new jobs can cause instability in the workshop, which may lead to additional costs, operator fatigue, increased risk of errors, and customer dissatisfaction. Several metrics have been used to measure instability. These metrics can be conflicting, and their choice depends on the user. In this paper, we conduct an analysis considering the DM’s preferences regarding stability criteria, and assume that he expresses his preferences in the form of judgments (e.g. very good, good, average, or bad). Our formulation of stability criteria allows the DMs to interpret the solutions. The solutions potentially accepted by the DM need to excel in the efficiency criterion while achieving at least good quality on the stability criteria. We aggregate the decision-maker’s preferences on stability criteria using a sorting preference model called MRSort. We propose two approaches for integrating the DM’s preferences into the optimization process: an a priori approach and an interactive approach. We show that with the a priori approach, we are able to find solutions of at least good quality on 96% of small instances, 93% of medium instances, and 59% of large instances, but this can lead to losses in efficiency. With the interactive approach, we obtain solutions of at least good category in about 59% of instances for each size, but it requires multiple interactions if one aims to achieve solutions of at least good quality. This highlights the conflicting nature between efficiency and stability. The optimization is performed using a Variable Neighborhood Search with three types of neighborhood structures for local search.