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CON/SLK due date assignment and scheduling on a single machine with two agents

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  • Yunqiang Yin
  • Du‐Juan Wang
  • Chin‐Chia Wu
  • T.C.E. Cheng

Abstract

We consider scheduling problems involving two agents (agents A and B), each having a set of jobs that compete for the use of a common machine to process their respective jobs. The due dates of the A‐jobs are decision variables, which are determined by using the common (CON) or slack (SLK) due date assignment methods. Each agent wants to minimize a certain performance criterion depending on the completion times of its jobs only. Under each due date assignment method, the criterion of agent A is always the same, namely an integrated criterion consisting of the due date assignment cost and the weighted number of tardy jobs. Several different criteria are considered for agent B, including the maxima of regular functions (associated with each job), the total (weighted) completion time, and the weighted number of tardy jobs. The overall objective is to minimize the performance criterion of agent A, while keeping the objective value of agent B no greater than a given limit. We analyze the computational complexity, and devise polynomial or pseudo‐polynomial dynamic programming algorithms for the considered problems. We also convert, if viable, any of the devised pseudopolynomial dynamic programming algorithms into a fully polynomial‐time approximation scheme. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 416–429, 2016

Suggested Citation

  • Yunqiang Yin & Du‐Juan Wang & Chin‐Chia Wu & T.C.E. Cheng, 2016. "CON/SLK due date assignment and scheduling on a single machine with two agents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(5), pages 416-429, August.
    • Handle: RePEc:wly:navres:v:63:y:2016:i:5:p:416-429
    DOI: 10.1002/nav.21700
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    Cited by:

    1. Baruch Mor, 2022. "Minmax common flow-allowance problems with convex resource allocation and position-dependent workloads," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 79-97, January.
    2. Hongyu He & Yanzhi Zhao & Xiaojun Ma & Zheng-Guo Lv & Ji-Bo Wang, 2023. "Branch-and-Bound and Heuristic Algorithms for Group Scheduling with Due-Date Assignment and Resource Allocation," Mathematics, MDPI, vol. 11(23), pages 1-14, November.
    3. Sang, Yao-Wen & Wang, Jun-Qiang & Sterna, Małgorzata & Błażewicz, Jacek, 2023. "Single machine scheduling with due date assignment to minimize the total weighted lead time penalty and late work," Omega, Elsevier, vol. 121(C).
    4. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    5. Lei Pan & Xinyu Sun & Ji-Bo Wang & Li-Han Zhang & Dan-Yang Lv, 2023. "Due date assignment single-machine scheduling with delivery times, position-dependent weights and deteriorating jobs," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-16, May.
    6. Shisheng Li & T.C.E. Cheng & C.T. Ng & Jinjiang Yuan, 2017. "Two‐agent scheduling on a single sequential and compatible batching machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(8), pages 628-641, December.
    7. Shesh Narayan Sahu & Yuvraj Gajpal & Swapan Debbarma, 2018. "Two-agent-based single-machine scheduling with switchover time to minimize total weighted completion time and makespan objectives," Annals of Operations Research, Springer, vol. 269(1), pages 623-640, October.
    8. Yunqiang Yin & Doudou Li & Dujuan Wang & T. C. E. Cheng, 2021. "Single-machine serial-batch delivery scheduling with two competing agents and due date assignment," Annals of Operations Research, Springer, vol. 298(1), pages 497-523, March.
    9. Yuan Zhang & Jinjiang Yuan, 2019. "A note on a two-agent scheduling problem related to the total weighted late work," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 989-999, April.
    10. Chen, Ke & Cheng, T.C.E. & Huang, Hailiang & Ji, Min & Yao, Danli, 2023. "Single-machine scheduling with autonomous and induced learning to minimize total weighted number of tardy jobs," European Journal of Operational Research, Elsevier, vol. 309(1), pages 24-34.
    11. Baruch Mor & Gur Mosheiov, 2021. "Minmax due-date assignment on a two-machine flowshop," Annals of Operations Research, Springer, vol. 305(1), pages 191-209, October.
    12. Maliheh Ganji & Rahmat Rabet & Seyed Mojtaba Sajadi, 2022. "A new coordinating model for green supply chain and batch delivery scheduling with satisfaction customers," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(4), pages 4566-4601, April.
    13. Dujuan Wang & Yugang Yu & Huaxin Qiu & Yunqiang Yin & T. C. E. Cheng, 2020. "Two‐agent scheduling with linear resource‐dependent processing times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 573-591, October.
    14. Yunqiang Yin & Yongjian Yang & Dujuan Wang & T.C.E. Cheng & Chin‐Chia Wu, 2018. "Integrated production, inventory, and batch delivery scheduling with due date assignment and two competing agents," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(5), pages 393-409, August.
    15. Shabtay, Dvir & Mosheiov, Gur & Oron, Daniel, 2022. "Single machine scheduling with common assignable due date/due window to minimize total weighted early and late work," European Journal of Operational Research, Elsevier, vol. 303(1), pages 66-77.
    16. Li-Han Zhang & Dan-Yang Lv & Ji-Bo Wang, 2023. "Two-Agent Slack Due-Date Assignment Scheduling with Resource Allocations and Deteriorating Jobs," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    17. Byung-Cheon Choi & Myoung-Ju Park, 2020. "Scheduling two projects with controllable processing times in a single-machine environment," Journal of Scheduling, Springer, vol. 23(5), pages 619-628, October.
    18. Yuan Zhang & Jinjiang Yuan & Chi To Ng & Tai Chiu E. Cheng, 2021. "Pareto‐optimization of three‐agent scheduling to minimize the total weighted completion time, weighted number of tardy jobs, and total weighted late work," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 378-393, April.
    19. Dvir Shabtay, 2023. "A new perspective on single-machine scheduling problems with late work related criteria," Annals of Operations Research, Springer, vol. 322(2), pages 947-966, March.
    20. Yunqiang Yin & Youhua Chen & Kaida Qin & Dujuan Wang, 2019. "Two-agent scheduling on unrelated parallel machines with total completion time and weighted number of tardy jobs criteria," Journal of Scheduling, Springer, vol. 22(3), pages 315-333, June.

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