An Efficient Algorithm for Solving the Flexible Job Shop Scheduling Problem

Purpose To investigate the efficiency of a discretization procedure utilizing a time-indexed mathematical optimization model for finding accurate solutions to flexible job shop scheduling problems considering objectives comprising makespan and tardiness, respectively. Design/methodology/approach A time-indexed mixed integer programming model is used to find solutions by iteratively employing time steps of decreasing length. The solutions and computation times are compared with results from a known benchmark formulation and an alternative model. Findings The proposed method finds significantly better solutions for the largest instances within the same time frame. Both the other models are better choices for some smaller instances, which is expected since the new method is designed for larger problems. Only our alternative model is able to solve two of the largest instances when minimizing the tardiness. Research limitations/implications Interesting future research topics include the introduction of constraints representing other relevant entities such as the availability of tools and fixtures, and the scheduling of maintenance activities and personnel. Practical implications Real cases of flexible job shop problems typically yield very large models. Since the new procedure quickly finds solutions of good quality to such instances, our findings imply that the new procedure is beneficially utilized for scheduling real flexible job shops. Original/value We show that real flexible job shop problems can be solved through the solution of a series of carefully formulated discretized mathematical optimization models.