Scheduling a deteriorating maintenance activity and due-window assignment

Several papers published during the last decade dealt with scheduling a maintenance activity and considered a new setting, where the maintenance duration is assumed to be deteriorating, i.e., it requires more time or effort if it is delayed. We study a deteriorating maintenance in the context of due-window assignment, where a time interval is determined such that jobs completed within this interval are “ontime”, whereas early and tardy jobs are penalized. Thus, our paper extends known models by considering simultaneously a deteriorating maintenance and due-window. Two deterioration types are considered: time-dependent (where the maintenance time increases as a function of its starting time), and position-dependent (where it is a function of its position in the sequence). The classical assumption of position-independent processing times was considered first, and then the model is extended to general position-dependent processing times. We prove several properties of the optimal timing of the duewindow and of the maintenance. Consequently, we show that all the problems studied here are solved in Oðn4Þ, where n is the number of jobs. & 2014 Elsevier Ltd. All rights reserved.