Coordinated order scheduling and outsourcing on dedicated parallel machines

IF 6 2区管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

European Journal of Operational Research Pub Date : 2025-09-08 DOI:10.1016/j.ejor.2025.08.035

Jinwen Ou, Weidong Li, Xueling Zhong

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引用次数: 0

Abstract

In this paper we investigate two order scheduling problems with bundled operations on m dedicated parallel machines when outsourcing is allowed. In the first problem, the objective is to minimize the makespan of the accepted jobs (orders) subject to the constraint that the total rejection (outsourcing) cost is no more than a budget. In the second problem, the objective is to minimize the makespan of accepted jobs plus the total rejection cost of rejected jobs. We show that the first problem cannot be approximated within a factor less than 2 in polynomial time, unless P = NP. For each of the two problems when m is fixed, we present a quasi-linear-time FPTAS (fully polynomial time approximation scheme). For the second problem when m=2, we develop a faster FPTAS by an interesting problem transformation and advanced rounding method.

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在专用的并行机器上协调订单调度和外包

在允许外包的情况下，研究了m台专用并行机上捆绑作业的两个订单调度问题。在第一个问题中，目标是在总拒绝（外包）成本不超过预算的约束下，将接受的工作（订单）的完工时间最小化。在第二个问题中，目标是最小化被接受作业的完工时间加上被拒绝作业的总拒绝成本。我们证明了第一个问题不能在多项式时间内小于2的因子内逼近，除非P = NP。对于m固定时的两个问题，我们分别给出了一个准线性时间FPTAS（全多项式时间近似方案）。对于第二个问题，当m=2时，我们通过有趣的问题变换和先进的舍入方法开发了一个更快的FPTAS。

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

European Journal of Operational Research 管理科学-运筹学与管理科学

CiteScore

11.90

自引率

9.40%

发文量

786

审稿时长

8.2 months

期刊介绍： The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.