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Single-Machine Scheduling Problems with Variable Processing Times and Past-Sequence-Dependent Delivery Times

Author

Listed:
  • Ji-Bo Wang

    (School of Science, Shenyang Aerospace University, Shenyang, P. R. China)

  • Jing Xue

    (School of Science, Shenyang Aerospace University, Shenyang, P. R. China)

  • Bo Cui

    (School of Science, Shenyang Aerospace University, Shenyang, P. R. China)

  • Ming Gao

    (School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian 116025, P. R. China)

Abstract

Scheduling problems with variable processing times and past-sequence-dependent delivery times are considered on a single-machine. The delivery times of jobs depend on their waiting times of processing. A job’s actual processing time depends on its position in a sequence, its starting time and its allocation of non-renewable resources. Under the linear resource consumption function, the goal (version) is to determine the optimal sequence and optimal resource allocation such that the sum of scheduling cost and total resource consumption cost is minimized. Under the convex resource consumption function, three versions of the scheduling cost and total resource consumption cost are discussed. We prove that these four versions can be solved in polynomial time, respectively. Some applications are also given by using the scheduling cost, which involve the makespan, total completion time, total absolute differences in completion times (TADC), and total absolute differences in waiting times (TADW).

Suggested Citation

  • Ji-Bo Wang & Jing Xue & Bo Cui & Ming Gao, 2022. "Single-Machine Scheduling Problems with Variable Processing Times and Past-Sequence-Dependent Delivery Times," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 39(02), pages 1-18, April.
    • Handle: RePEc:wsi:apjorx:v:39:y:2022:i:02:n:s0217595921500135
    DOI: 10.1142/S0217595921500135
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