Journal of Scheduling

, Volume 18, Issue 1, pp 3–13 | Cite as

Optimal delivery time quotation in supply chains to minimize tardiness and delivery costs

  • Sorina Dumitrescu
  • George Steiner
  • Rui Zhang


There are many situations when, due to unexpected delays, the supplier may not be able to deliver some orders by the promised due dates. We present a model for quoting attainable delivery times to minimize tardiness penalties and delivery costs, when deliveries take place in batches. We show that the general problem is strongly \({\mathcal {NP}}\)-hard, but when all orders have the same per-unit due-date-assignment cost, it is \({\mathcal {NP}}\)-hard only in the ordinary sense. For the latter case, we present a pseudo-polynomial algorithm, which is converted into a fully polynomial-time approximation scheme. If the tardiness penalties are also identical, we show that the problem can be solved in polynomial time.


Scheduling Tardiness Delivery times Approximation algorithm 



This research was supported in part by NSERC Discovery Grant 1708-09.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringMcMaster UniversityHamiltonCanada
  2. 2.Operations Management Area, DeGroote School of BusinessMcMaster UniversityHamiltonCanada

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