系统管理学报

Journal of Systems & Management ›› 2026, Vol. 35 ›› Issue (2): 407-421.DOI: 10.3969/j.issn.2097-4558.2026.02.008

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Identical Parallel Machine Scheduling Problem Considering Shared Machine Rental Discounts

ZHI Rongteng1, XU Yinfeng2, ZHENG Feifeng3, LIU Ming4   

  1. 1. School of Economics and Management, Qilu Normal University, Jinan 250200, China; 2. School of Management, Xi’an Jiaotong University, Xi’an 710049, China; 3. Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China; 4. School of Economics and Management, Tongji University, Shanghai 200092, China
  • Received:2022-07-04 Revised:2024-04-12 Online:2026-03-28 Published:2026-04-14

考虑共享机器租赁折扣的同型机调度问题

智荣腾1，徐寅峰2，郑斐峰3，刘明4   

  1. 1.齐鲁师范学院 经济与管理学院，济南 250200；2.西安交通大学 管理学院，西安 710049；
    3.东华大学 旭日工商管理学院，上海 200051；4.同济大学 经济管理学院，上海 200092
  • 基金资助:
    国家自然科学基金资助项目（71832001，72271051，72071144）；中央高校基本科研专项资金资助项目（2232018H-07）

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Abstract: Against the backdrop of China’s vigorous promotion of shared manufacturing, rapid transformation and upgrading of manufacturing enterprises and the scientific design of sharing schemes have become important research topics. This paper focuses on the shared scheduling of machine resources in manufacturing enterprises. By considering characteristics such as fixed rental costs, unit variable rental costs, and shared-machine discount policies, it constructs a mathematical programming model with the objective of minimizing the sum of the maximum makespan and the total shared-machine rental cost. It examines two scenarios: identical and non-identical processing times. For the case of identical processing times, it derives key properties of the optimal schedule and designs an exact algorithm. For the case of non-identical processing times, it establishes a lower bound and proposes a 4/3-approximation algorithm. Finally, it conducts numerical experiments to verify the effectiveness of both algorithms. The results provide scientific decision-making support for machine resource sharing practices and production scheduling management in manufacturing enterprises.

Key words: shared machine, rental discounts, parallel machine scheduling, makespan

摘要： 在我国全力推进共享制造的背景下，制造企业的快速转型升级与共享方案的科学设计已成为重要的研究课题。本文以制造企业机器资源的共享调度为切入点，结合共享机器的固定租赁成本、单位可变租赁成本及共享优惠折扣等特征，构建了以最小化最大完工时间与共享机器总租赁成本之和为目标的数学规划模型。研究重点分析了工件加工时长相同与不同两种情形下调度策略的差异：针对加工时长相同的情形，推导了最优调度的关键性质并设计了精确算法；针对加工时长不同的情形，给出了问题的下界并提出了近似比为4/3的近似算法。最后，通过数值实验验证了两类算法的有效性。本研究成果可为制造企业的机器资源共享实践与生产调度管理提供科学决策支持。

关键词: 共享机器, 租赁折扣, 平行机调度, 最大完工时间

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