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Scheduling with two competing agents to minimize total weighted earliness

Author

Listed:
  • Enrique Gerstl

    (The Hebrew University
    Jerusalem College of Technology)

  • Baruch Mor

    (Ariel University)

  • Gur Mosheiov

    (The Hebrew University)

Abstract

We study a single machine scheduling problem with two competing agents and earliness measures. Given a common deadline for all the jobs of both agents, the objective function is minimizing the total weighted earliness of the first agent, subject to an upper bound on the maximum earliness of the jobs of the second agent. This problem was recently proved to be NP-hard, leaving the question of the complexity class open. We introduce a pseudo-polynomial dynamic programming algorithm, implying that the problem is NP-hard in the ordinary sense. An extensive numerical study indicates that the dynamic programming is very effective for solving medium size instances. We also propose an efficient heuristic, which is shown numerically to produce very close-to-optimal schedules. The dynamic programming algorithm is extended to any (given) number of agents, proving NP-hardness in the ordinary sense of the general multi-agent setting. Finally, we study the inverse problem of minimizing the maximum earliness of one agent subject to an upper bound on the maximum total weighted earliness of the second agent. We introduce a pseudo-polynomial dynamic programming algorithm, a simple greedy-type heuristic and a lower bound. Our numerical tests verify that the heuristic produces very small optimality gaps.

Suggested Citation

  • Enrique Gerstl & Baruch Mor & Gur Mosheiov, 2017. "Scheduling with two competing agents to minimize total weighted earliness," Annals of Operations Research, Springer, vol. 253(1), pages 227-245, June.
    • Handle: RePEc:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2310-5
    DOI: 10.1007/s10479-016-2310-5
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    References listed on IDEAS

    as
    1. Mor, Baruch & Mosheiov, Gur, 2010. "Scheduling problems with two competing agents to minimize minmax and minsum earliness measures," European Journal of Operational Research, Elsevier, vol. 206(3), pages 540-546, November.
    2. Allesandro Agnetis & Pitu B. Mirchandani & Dario Pacciarelli & Andrea Pacifici, 2004. "Scheduling Problems with Two Competing Agents," Operations Research, INFORMS, vol. 52(2), pages 229-242, April.
    3. Wan, Guohua & Vakati, Sudheer R. & Leung, Joseph Y.-T. & Pinedo, Michael, 2010. "Scheduling two agents with controllable processing times," European Journal of Operational Research, Elsevier, vol. 205(3), pages 528-539, September.
    4. Oron, Daniel & Shabtay, Dvir & Steiner, George, 2015. "Single machine scheduling with two competing agents and equal job processing times," European Journal of Operational Research, Elsevier, vol. 244(1), pages 86-99.
    5. Cheng, Shuenn-Ren, 2014. "Some new problems on two-agent scheduling to minimize the earliness costs," International Journal of Production Economics, Elsevier, vol. 156(C), pages 24-30.
    6. Alessandro Agnetis & Dario Pacciarelli & Andrea Pacifici, 2007. "Multi-agent single machine scheduling," Annals of Operations Research, Springer, vol. 150(1), pages 3-15, March.
    7. Mor, Baruch & Mosheiov, Gur, 2011. "Single machine batch scheduling with two competing agents to minimize total flowtime," European Journal of Operational Research, Elsevier, vol. 215(3), pages 524-531, December.
    8. Shuenn-Ren Cheng, 2014. "Scheduling Two-Agents with a Time-Dependent Deterioration to Minimize the Minsum Earliness Measures," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-10.
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    Cited by:

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