Unrelated parallel-machine scheduling problems with aging effects and deteriorating maintenance activities

This paper explores the problems of unrelated parallel-machine scheduling with aging effects and deteriorating maintenance activities. The jobs are non-resumable. Each machine has at most one maintenance activity which is allowed throughout the planning horizon. Assume that once the maintenance activity is completed, the functions of machine and the properties of jobs e.g. the temperature (hardness) of materials that processed by the machine will be restored to their initial conditions. The length of the maintenance activity is a linear function of its starting time. The objectives of this study are to minimize the total completion time and the total machine load. Three basic types of aging effect model are proposed. We show that all the proposed models can be solved optimally in polynomial time.