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Optimal Different Due-Date Assignment Scheduling with Group Technology and Resource Allocation

Author

Listed:
  • Xuyin Wang

    (Business School, Northwest Normal University, Lanzhou 730070, China)

  • Weiguo Liu

    (Business School, Northwest Normal University, Lanzhou 730070, China)

Abstract

In this paper, we consider different due-date assignment scheduling with group technology and resource allocation on a single machine, where the due date of each job may be different. Under constant processing times, the objective function is to minimize the scheduling cost (i.e., the weighted sum of earliness, tardiness, and due-date assignment cost, where the weights are position dependent). Under some optimal properties, we prove that this problem can be solved in O ( ζ log ζ ) time, where ζ is the number of jobs. The problem is also extended to cases which include linear and convex functions of the quantity of resource allocation. The objective function is minimizing the sum of the scheduling cost and the resource-consumption cost. For the special case of linear and convex functions, we show that the problem is polynomially solvable in O ( ζ 3 ) time.

Suggested Citation

  • Xuyin Wang & Weiguo Liu, 2024. "Optimal Different Due-Date Assignment Scheduling with Group Technology and Resource Allocation," Mathematics, MDPI, vol. 12(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:436-:d:1329090
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    References listed on IDEAS

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    1. Ying Chen & Xiaole Ma & Guiqing Zhang & Yongxi Cheng, 2023. "On optimal due date assignment without restriction and resource allocation in group technology scheduling," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-19, March.
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    5. Clyde L. Monma & Alexander Schrijver & Michael J. Todd & Victor K. Wei, 1990. "Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 736-748, November.
    6. 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.
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