An online joint replenishment problem combined with single machine scheduling

Györgyi, Péter and Kis, Tamás and Tamási, Tímea (2023) An online joint replenishment problem combined with single machine scheduling. JOURNAL OF COMBINATORIAL OPTIMIZATION, 45 (5). ISSN 1382-6905 10.1007/s10878-023-01064-z


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This paper considers a combination of the joint replenishment problem with single machine scheduling. There is a single resource, which is required by all the unit-time jobs, and a job can be started at time point t on the machine if and only if the machine does not process another job at t , and the resource is replenished between its release date and t . Each replenishment has a cost, which is independent of the amount replenished. The objective is to minimize the total replenishment cost plus the maximum flow time of the jobs. We consider the online variant of the problem, where the jobs are released over time, and once a job is inserted into the schedule, its starting time cannot be changed. We propose a deterministic 2-competitive online algorithm for the general input. Moreover, we show that for a certain class of inputs (so-called p -bounded input), the competitive ratio of the algorithm tends to \sqrt{2} 2 as the number of jobs tends to infinity. We also derive several lower bounds for the best competitive ratio of any deterministic online algorithm under various assumptions.

Item Type: Article
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Divisions: Research Laboratory on Engineering & Management Intelligence
SWORD Depositor: MTMT Injector
Depositing User: MTMT Injector
Date Deposited: 28 Aug 2023 07:03
Last Modified: 11 Sep 2023 14:56

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