Two-machine job shop scheduling with optional job rejection

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED Optimization Letters Pub Date : 2023-12-06 DOI:10.1007/s11590-023-02077-7

Ren-Xia Chen, Shi-Sheng Li

引用次数: 0

Abstract

We investigate a two-machine job shop scheduling problem with optional job rejection. The target is to look for a feasible schedule for the set of accepted jobs so that the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs is minimized. We propose an exact pseudo-polynomial dynamic programming algorithm, a greedy \(\frac{\sqrt{5}+1}{2}\)-approximation algorithm, an LP-based \(\frac{e}{e-1}\)-approximation algorithm, and a fully polynomial time approximation scheme to solve it. We demonstrate that the proportionate case is \(\mathcal{N}\mathcal{P}\)-hard and provide an \(O(n^2)\)-time algorithm for the agreeable case.

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具有可选作业拒绝的双机作业车间调度

研究了具有可选拒绝的双机作业车间调度问题。目标是为一组可接受的作业寻找一个可行的调度，使可接受作业的最大完工时间和被拒绝作业的总罚金最小。我们提出了一个精确伪多项式动态规划算法，一个贪婪的\(\frac{\sqrt{5}+1}{2}\) -逼近算法，一个基于lp的\(\frac{e}{e-1}\) -逼近算法，以及一个全多项式时间逼近方案来求解它。我们证明了比例情况是\(\mathcal{N}\mathcal{P}\) -困难的，并提供了一种\(O(n^2)\)时间算法来处理符合条件的情况。

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

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.