Single-machine scheduling with an external resource

• Published in: European journal of operational research Vol. 293; no. 2; pp. 457 - 468
• Main Authors: Briskorn, Dirk, Davari, Morteza, Matuschke, Jannik
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2021
• Subjects: Complexity; External resource; Pseudo-polynomial algorithm; Scheduling; Single-machine scheduling; Single-machine scheduling; Pseudo-polynomial algorithm; Scheduling; External resource; Complexity
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2020.12.045

highlights•We study single-machine scheduling with an external resource.•We look at four different classes of problems with an external resource.•For each class, we consider four different classical objective functions.•We provide a complexity analysis for different members of these four classes. This paper studies the complexity of single-machine scheduling with an external resource, which is rented for a non-interrupted period. Jobs that need this external resource are executed only when the external resource is available. There is a cost associated with the scheduling of jobs and a cost associated with the duration of the renting period of the external resource. We look at four classes of problems with an external resource: a class of problems where the renting period is budgeted and the scheduling cost needs to be minimized, a class of problems where the scheduling cost is budgeted and the renting period needs to be minimized, a class of two-objective problems where both, the renting period and the scheduling cost, are to be minimized, and a class of problems where a linear combination of the scheduling cost and the renting period is minimized. We provide a thorough complexity analysis (NP-hardness proofs and (pseudo-)polynomial algorithms) for different members of these four classes.