Single machine scheduling with general positional deterioration and rate-modifying maintenance

Combining time and position dependent effects on a single machine subject to rate-modifying activities

“…In our paper [1], we present a brief account on scheduling with maintenance, stating that the most natural range of models that use machine maintenance to restore deteriorating processing conditions, fully or at least partially, have appeared only recently, see, e.g., [13] and [14]. The duration of a maintenance period can either be a given constant or be dependent on its start time.…”

“…With several maintenance periods in a schedule, the jobs are split into several groups, one group before the first maintenance and one after each maintenance period. An important enhancement of the concept of maintenance is done in [1], in which the authors do not assume that all maintenance periods are identical and allow each one of them to leave the processing conditions of the machine in a different state, not necessarily bringing them back to an initial perfect state. In this paper, we go further and deal with a more general concept of a rate-modifying activity performed on a machine, which is not limited to machine maintenance but may influence the processing of the jobs in the group that follows such an activity.…”

“…We refer to such effects as group-dependent effects. As shown in [1], combining machine maintenance with group-dependent positional deterioration still allows solving the corresponding scheduling problem in polynomial time. Our third message addresses the main issue of this paper: combining the general machine maintenance, or rather, rate-modifying activities, with enhanced job-independent group-dependent effects.…”

“…Since the RMPs can be different in nature, we need a model that is capable of handling situations, in which the effects are group-dependent, so that jobs sequenced in different groups are subject to different effects. Group-dependent effects have been first introduced in [1], with the focus on single machine models with positional deterioration effects and the RMPs to be strictly maintenance periods, i.e., aimed at improving the processing conditions, but not necessarily fully restoring them. Extensions of the multi-maintenance model to parallel machines can be found in [2].…”

“…This paper can be seen as a continuation of our recent publications [1] and [2]. In this introduction, we do not attempt to give a historical account of the area, which can be found in the review [2].…”