Single machine rescheduling for new orders: properties and complexity results

TL;DR

This paper studies how to efficiently integrate new jobs into existing schedules on a single machine, analyzing properties, classifications, and the computational complexity of various rescheduling problems with disruption constraints.

Contribution

It provides a classification of idle and no-idle rescheduling problems and establishes the complexity of five previously unresolved problems.

Findings

Classified rescheduling problems into idle and no-idle categories.

Proved complexity results for five open problems in the literature.

Analyzed the impact of disruption constraints on schedule structure.

Abstract

Rescheduling problems arise in a variety of situations where a previously planned schedule needs to be adjusted to deal with unforeseen events. A common problem is the arrival of new orders, i.e. jobs, which have to be integrated into the schedule of the so-called old jobs. The maximum and total absolute time deviations of the completion times of these jobs are modeled as a disruption constraint to limit the change in the original schedule. Disruption constraints affect the shape of an optimal schedule, particularly with respect to the sequencing of old jobs and the insertion of idle time. We therefore give a classification into idle and no-idle problems for a set of single-machine rescheduling problems with different objective functions. We then prove the complexity of five rescheduling problems that have been left open in the literature.