Scheduling algorithms for multi-stage flow shops with reworks under overlapped queue time limits

This study addresses a multi-stage flow shop scheduling problem in which a job is reworked when its queue time between two arbitrary stages exceeds an upper limit. The problem is to determine the start times of jobs and rework setups/operations if incurred for the objective of minimising makespan. As an extension of the previous studies, multiple overlapped queue time limits are considered, i.e. some in-between stages of queue time limits for a job are overlapped. A mixed integer programming model is developed and its performance is reported for small-sized test instances. Then, due to the limited applications of optimal solution approaches, a variable neighbourhood search (VNS) algorithm is proposed that generates an initial solution and improves it using a shaking and a local search improvement methods. In addition, it is extended to the general variable neighbourhood search (GVNS) algorithms with variable neighbourhood descent (VND) methods. Computational results show that the GVNS algorithms outperform the VNS algorithm significantly and also give near optimal solutions for small-sized test instances within a reasonable amount of computation times.