Publisher DOI: 10.1007/978-3-030-53262-8_14
arXiv ID: 1911.12138
Title: Scheduling with non-renewable resources: Minimizing the sum of completion times
Language: English
Authors: Bérczi, Kristóf 
Király, Tamás 
Omlor, Simon 
Keywords: Approximation algorithm; Non-renewable resources; PTAS; Scheduling
Issue Date: May-2020
Publisher: Springer
Source: International Symposium on Combinatorial Optimization (ISCO 2020)
Abstract (english): 
We consider single-machine scheduling problems with a non-renewable resource. In this setting, there are n jobs, each characterized by a processing time, a weight, and a resource requirement. At given points in time, certain amounts of the resource are made available to be consumed by the jobs. The goal is to assign the jobs non-preemptively to time slots on the machine, so that each job has the required resource amount available at the start of its processing. We consider the objective of minimizing the weighted sum of completion times. The main contribution of the paper is a PTAS for the case of 0 processing times (formula presented). In addition, we show strong NP-hardness of the case of unit resource requirements and weights (formula presented), thus answering an open question of Györgyi and Kis. We also prove that the schedule corresponding to the Shortest Processing Time First ordering provides a 3/2-approximation for the latter problem.
Conference: 6th International Symposium on Combinatorial Optimization (ISCO 2020) 
ISBN: 978-3-030-53262-8
ISSN: 0302-9743
Institute: Algorithmen und Komplexität E-11 
Document Type: Chapter/Article (Proceedings)
Project: Multivariate Algorithmen für Scheduling mit hoher Multiplizität 
Part of Series: Lecture notes in computer science 
Volume number: 12176 LNCS
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