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Scheduling with non-renewable resources: Minimizing the sum of completion times
Publikationstyp
Conference Paper
Date Issued
2020-05
Sprache
English
Author(s)
Institut
TORE-URI
First published in
Number in series
12176 LNCS
Start Page
167
End Page
178
Citation
6th International Symposium on Combinatorial Optimization (ISCO 2020): 167-178
Contribution to Conference
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Springer
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.
Subjects
Approximation algorithm
Non-renewable resources
PTAS
Scheduling
DDC Class
510: Mathematik