Single machine scheduling with the total weighted late work and rejection cost

IF 1.9 4区管理学 Q3 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Naval Research Logistics Pub Date : 2024-08-15 DOI:10.1002/nav.22222

Yao‐Wen Sang, Jun‐Qiang Wang, Małgorzata Sterna, Jacek Błażewicz

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Abstract

We study a single machine scheduling problem with the total weighted late work and the total rejection cost. The late work of a job is the part of this job executed after its due date, and the rejection cost of a job is the fee of rejecting to process it. We consider a Pareto scheduling and two restricted scheduling problems. The Pareto scheduling problem aims to find all non‐dominated values of the total weighted late work and the total rejection cost. The restricted scheduling problems are dedicated to minimizing the total weighted late work with the total rejection cost not greater than a given threshold, and minimizing the total rejection cost with the total weighted late work not greater than a given threshold, respectively. For the Pareto scheduling problem, we prove that it is binary NP‐hard by providing a pseudo‐polynomial time algorithm, and give a fully polynomial time approximation scheme (FPTAS). For the restricted scheduling problems, we prove that there are no FPTASes unless , which answers an open problem. Moreover, we develop relaxed FPTASes for these two restricted scheduling problems.

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利用总加权延迟工作和拒绝成本进行单机调度

我们研究的是单机调度问题中的总加权延迟工作和总拒绝成本。一项作业的延迟工作是指该作业在到期日之后执行的部分，而一项作业的拒绝成本是指拒绝处理该作业的费用。我们考虑了一个帕累托调度问题和两个限制性调度问题。帕累托调度问题的目的是找到总加权延迟工作和总拒绝成本的所有非支配值。受限调度问题则分别致力于在总拒绝成本不大于给定阈值的情况下使总加权延迟工作量最小化，以及在总加权延迟工作量不大于给定阈值的情况下使总拒绝成本最小化。对于帕累托调度问题，我们通过提供一种伪多项式时间算法证明它是二元 NP 难问题，并给出了一种全多项式时间近似方案（FPTAS）。对于受限调度问题，我们证明除非，否则不存在 FPTAS，这回答了一个未决问题。此外，我们还为这两个受限调度问题开发了松弛的 FPTASes。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Naval Research Logistics 管理科学-运筹学与管理科学

CiteScore

4.20

自引率

4.30%

发文量

审稿时长

8 months

期刊介绍： Submissions that are most appropriate for NRL are papers addressing modeling and analysis of problems motivated by real-world applications; major methodological advances in operations research and applied statistics; and expository or survey pieces of lasting value. Areas represented include (but are not limited to) probability, statistics, simulation, optimization, game theory, quality, scheduling, reliability, maintenance, supply chain, decision analysis, and combat models. Special issues devoted to a single topic are published occasionally, and proposals for special issues are welcomed by the Editorial Board.