Approximation algorithms for the W-prize-collecting scheduling problem on a single machine with submodular rejection penalties

Tianjiao Guo (), Wen Liu (), Gengsheng Zhang () and Bo Hou ()
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Tianjiao Guo: Hebei Normal University
Wen Liu: Hebei Normal University
Gengsheng Zhang: Hebei Normal University
Bo Hou: Hebei Normal University

Journal of Combinatorial Optimization, 2025, vol. 49, issue 5, No 4, 13 pages

Abstract: Abstract In this paper, we consider the W-prize-collecting scheduling problem on a single machine with submodular rejection penalties. In this problem, we are given one machine, n jobs and a value W. Every job has a processing time and a profit. Each job is either accepted and processed on the machine, or rejected and a rejection penalty is paid. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalties of the rejected jobs which is determined by a submodular function, provided that the total profit of the accepted jobs is at least W. Under the assumption that the submodular penalty function is polymatriod, we design a 2-approximation algorithm based on the primal-dual framework.

Keywords: Scheduling problem; Submodular rejection penalty; W-prize-collecting; Approximation algorithm; Primal-dual (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01314-2

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