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Study on Single-Machine Common/Slack Due-Window Assignment Scheduling with Delivery Times, Variable Processing Times and Outsourcing

Author

Listed:
  • Bing Bai

    (School of Economics and Management, Shenyang Aerospace University, Shenyang 110136, China
    These authors have contributed equally to this work.)

  • Cai-Min Wei

    (School of Mathematics and Computer, Shantou University, Shantou 515063, China
    These authors have contributed equally to this work.)

  • Hong-Yu He

    (School of Economics, Shenyang University, Shenyang 110096, China
    These authors have contributed equally to this work.)

  • Ji-Bo Wang

    (School of Economics and Management, Shenyang Aerospace University, Shenyang 110136, China
    These authors have contributed equally to this work.)

Abstract

Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O ( n 6 ) time, where n is the number of jobs.

Suggested Citation

  • Bing Bai & Cai-Min Wei & Hong-Yu He & Ji-Bo Wang, 2024. "Study on Single-Machine Common/Slack Due-Window Assignment Scheduling with Delivery Times, Variable Processing Times and Outsourcing," Mathematics, MDPI, vol. 12(18), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2883-:d:1478963
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    References listed on IDEAS

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    1. Panwalkar, S.S. & Koulamas, Christos, 2020. "Analysis of flow shop scheduling anomalies," European Journal of Operational Research, Elsevier, vol. 280(1), pages 25-33.
    2. Rong-Rong Mao & Yi-Chun Wang & Dan-Yang Lv & Ji-Bo Wang & Yuan-Yuan Lu, 2023. "Delivery Times Scheduling with Deterioration Effects in Due Window Assignment Environments," Mathematics, MDPI, vol. 11(18), pages 1-18, September.
    3. Baruch Mor, 2023. "Single machine scheduling problems involving job-dependent step-deterioration dates and job rejection," Operational Research, Springer, vol. 23(1), pages 1-19, March.
    4. Jin Qian & Yu Zhan, 2022. "The Due Window Assignment Problems with Deteriorating Job and Delivery Time," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    5. Shi-Sheng Li & Ren-Xia Chen, 2023. "Competitive two-agent scheduling with release dates and preemption on a single machine," Journal of Scheduling, Springer, vol. 26(3), pages 227-249, June.
    6. 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.
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