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arXiv · 2406.08104

Resource Leveling: Complexity of a UET two-processor scheduling variant and related problems

Pascale Bendotti·Luca Brunod Indrigo·Philippe Chrétienne·Bruno Escoffier
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Abstract

This paper mainly focuses on a resource leveling variant of a two-processor scheduling problem. The latter problem is to schedule a set of dependent UET jobs on two identical processors with minimum makespan. It is known to be polynomial-time solvable. In the variant we consider, the resource constraint on processors is relaxed and the objective is no longer to minimize makespan. Instead, a deadline is imposed on the makespan and the objective is to minimize the total resource use exceeding a threshold resource level of two. This resource leveling criterion is known as the total overload cost. Sophisticated matching arguments allow us to provide a polynomial algorithm computing the optimal solution as a function of the makespan deadline. It extends a solving method from the literature for the two-processor scheduling problem. Moreover, the complexity of related resource leveling problems sharing the same objective is studied. These results lead to polynomial or pseudo-polynomial algorithms or NP-hardness proofs, allowing for an interesting comparison with classical machine scheduling problems.

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Pascale Bendotti, Luca Brunod Indrigo, Philippe Chrétienne, Bruno Escoffier. 2024-06-12. Resource Leveling: Complexity of a UET two-processor scheduling variant and related problems. https://arxiv.org/abs/2406.08104

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