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Optimal multiple-breakpoint quantity discount schedules for customers with heterogeneous demands: all-unit or incremental?

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  • Rachel Chen
  • Lawrence Robinson

Abstract

The supplier's problem of designing a quantity discount schedule is much more complicated when she faces customers who vary in size. This article considers both all-unit and incremental discount schedules with multiple breakpoints that maximize the supplier's net savings. Specifically, we assume that the distribution of customers’ demand belongs to the general family of Bender's Pareto curves, which generalizes the well-known “80-20” rule from A-B-C inventory analysis. For any number of breakpoints, we prove that the supplier is at least as well off under the optimal incremental discount schedule as she would be under the optimal all-unit discount schedule. Numerical study shows that most of the savings can be captured by a modest number (five) of breakpoints and that the advantage of incremental schedules over all-unit schedules goes to zero as the number of breakpoints grows large.

Suggested Citation

  • Rachel Chen & Lawrence Robinson, 2012. "Optimal multiple-breakpoint quantity discount schedules for customers with heterogeneous demands: all-unit or incremental?," IISE Transactions, Taylor & Francis Journals, vol. 44(3), pages 199-214.
    • Handle: RePEc:taf:uiiexx:v:44:y:2012:i:3:p:199-214
    DOI: 10.1080/0740817X.2011.568038
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    Cited by:

    1. Nguyen, H.N. & Rainwater, C.E. & Mason, S.J. & Pohl, E.A., 2014. "Quantity discount with freight consolidation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 66(C), pages 66-82.
    2. Ponte, Borja & Puche, Julio & Rosillo, Rafael & de la Fuente, David, 2020. "The effects of quantity discounts on supply chain performance: Looking through the Bullwhip lens," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    3. Zhang, Guoqing & Shi, Jianmai & Chaudhry, Sohail S. & Li, Xindan, 2019. "Multi-period multi-product acquisition planning with uncertain demands and supplier quantity discounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 132(C), pages 117-140.
    4. Thunyarat Amornpetchkul, 2017. "Threshold discounts comparison: All-unit or incremental?," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 16(3), pages 265-294, June.

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