Rolling Scheduling by Hybrid Optimization Mixing Mathematical Programming and Meta-heuristics

—An Application to Machining Scheduling Problems

Abstract

This paper addresses the scheduling of an operator and a machine in the machining process. While both schedules are reduced to the job-shop type, the operator's completion time is relatively uncertain, so rolling scheduling is required. For problems with these characteristics, we apply relax-and-fix heuristics, in which some decision variables in each rolling are relaxed based on a mixed-integer programming model. Although the relax-and-fix heuristics can reduce the solution cost by mathematical programming, it may significantly reduce the optimality of the derived solution, depending on how the set of variables to be relaxed is selected. Therefore, we incorporate metaheuristics into the relax-and-fix heuristics to always choose the appropriate relaxation variables. The effectiveness of the proposed method is confirmed by applying it to real-world machining scheduling.