Improved Approaches to Minimize the Makespan on Single-Machine Scheduling with Periodic Preventive Maintenance Activities

Abstract

This paper addresses a single-machine scheduling problem with periodic preventive maintenance activities that are predeterministic so that the machine is not available all the time, and jobs have to be processed between two consecutive maintenance periods. We propose a mixed integer programming (MIP) model and two heuristics to minimize the makespan. With more constraints in our model, the model is more efficient than the recent model of Perez-Gonzalez and Framinan , and our model could solve problems with up to fifty jobs. Two heuristic algorithms, namely, H (MW) and H (LB∗), are also proposed, in which two bin-packing policies of the minimum waste and minimum lower bound are used, respectively. Furthermore, we also proposed an improvement procedure. The results showed that the heuristic H (MW) outperformed other heuristics of the paper, indicating that the bin-packing policy of the minimum waste is more effective than well-known ones such as full batch and best fit. Additionally, all the heuristic algorithms addressed in this paper combined with the improvement procedure could achieve a similar and high quality of solutions with a very tiny increase in computational expense.

Single-Machine Scheduling with Fixed Periodic Preventive Maintenance to Minimise the Total Weighted Completion Times

“…To minimise the makespan, Perez-Gonzalez and Framinan [16] developed an MIP model and two-phase heuristic algorithm based on binpacking dispatching rules to obtain optimal or near-optimal solutions. Zhou et al [17] also proposed different heuristic algorithms with a local improvement mechanism for the same problem.…”