Minimizing the Makespan on Parallel Machines with Flexible Maintenances and Dynamic Release Times of Jobs

Abstract

This paper considers the problem of scheduling n jobs and a number of preventive maintenances (PMs) on parallel machines to minimize the makespan. Each job has a release time, a processing time, and jobs could be continuously processed on the machine as long as the maximum allowed working time is not violated. The maximum allowed working time is given and the PMs are performed periodically once the maximum allowed working time is going to be violated. The problem is NP-hard due to the case of single machine has proven to be NP-hard. For the problem, a mixed integer programming (MIP) model is introduced and optimally solved small-size problems.