Scheduling with step learning and job rejection

Jiaxin Song, Cuixia Miao () and Fanyu Kong
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Jiaxin Song: Qufu Normal University
Cuixia Miao: Qufu Normal University
Fanyu Kong: Qufu Normal University

Operational Research, 2025, vol. 25, issue 1, No 6, 18 pages

Abstract: Abstract This paper focuses on job scheduling with step learning and job rejection. The step learning model aims to reduce the processing time for jobs starting after a specific learning date. Our objective is to minimize the sum of the maximum completion time of accepted jobs and the total rejection penalty of rejected jobs. We examine special cases of processing times for both single-machine and parallel-machine scenarios. For the former, we design a pseudo-polynomial time algorithm, a 2-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS) based on data rounding. For the latter, we present a fully polynomial-time approximation scheme achieved by trimming the state space. Additionally, for the general case of the single-machine problem, we propose a pseudo-polynomial time algorithm.

Keywords: Scheduling; Step learning; Rejection penalty; Pseudo-polynomial time algorithm; Fully polynomial-time approximation scheme; Approximation algorithm (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s12351-024-00887-w

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