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Scheduling with a due-window for acceptable lead-times

Author

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  • Enrique Gerstl

    (1] Jerusalem College of Technology, Jerusalem, Israel[2] The Hebrew University, Jerusalem, Israel)

  • Gur Mosheiov

    (The Hebrew University, Jerusalem, Israel)

Abstract

Due-dates are often determined during sales negotiations in two stages: (i) in the pre-sale stage, the customer provides a time interval (due-window) of his acceptable due-dates, (ii) in the second stage, the parties agree on the delivery penalties. Thus, the contract reflects penalties of both parts of the sales negotiations: earliness/tardiness penalties of the due-dates (as a function of the deviation from the agreed upon due-window), and earliness/tardiness penalties of the actual delivery times (as a function of the deviation from the due-dates). We model this setting of a two-stage negotiation on a single machine, and reduce the problem to a well-known setting of minimizing the weighted earliness/tardiness with a given (fixed) due-window. We adopt (and correct) a pseudo-polynomial dynamic programming algorithm for this NP-hard problem. The algorithm is extended to a setting of parallel identical machines, verifying that this case remains NP-hard in the ordinary sense. Moreover, an efficient greedy heuristic and a tight lower bound are introduced and tested. Extremely small optimality gaps are obtained in our numerical tests.

Suggested Citation

  • Enrique Gerstl & Gur Mosheiov, 2015. "Scheduling with a due-window for acceptable lead-times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(9), pages 1578-1588, September.
    • Handle: RePEc:pal:jorsoc:v:66:y:2015:i:9:p:1578-1588
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    Cited by:

    1. Yunqiang Yin & Du-Juan Wang & T C E Cheng & Chin-Chia Wu, 2016. "Bi-criterion single-machine scheduling and due-window assignment with common flow allowances and resource-dependent processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(9), pages 1169-1183, September.

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