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arXiv · 2006.03399

Single-machine scheduling with an external resource

Dirk Briskorn·Morteza Davari·Jannik Matuschke
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Abstract

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.

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Dirk Briskorn, Morteza Davari, Jannik Matuschke. 2020-06-05. Single-machine scheduling with an external resource. https://arxiv.org/abs/2006.03399

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