Scheduling with a due-window for acceptable lead-times

Enrique Gerstl and Gur Mosheiov
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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

Journal of the Operational Research Society, 2015, vol. 66, issue 9, 1578-1588

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.

Date: 2015
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