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On the use of break quantities in multi--echelon distribution systems

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  • Dekker, R.
  • Frenk, J.B.G.
  • Kleijn, M.J.
  • Piersma, N.
  • de Kok, T.G.

Abstract

In multi-echelon distribution systems it is usually assumed that demand is only satisfied from the lowest echelon. In this paper we will consider the case where demand can be satisfied from any level in the system. However, then the problem arises of how to allocate orders from customers to the different locations. A possible way of dealing with this problem consists of using a so-called break quantity rule. This easy implementable rule is to deliver every order with a size exceeding the break quantity from a higher echelon. The use of the break quantity rule now results in a reduction of the demand variability at the retailer and hence less safety stocks need to be held. The concept is studied for a two-echelon distribution system, consisting of one warehouse and one retailer, where the inventory at the retailer is controlled by an order up to level policy, and where at the warehouse there is enough inventory to satisfy all orders from the retailer and the customers. For this system an approximation for the long run average costs as a function of the break quantity is derived, and an algorithm is presented to determine the cost-optimal break quantity. Computational results indicate that the break quantity rule can lead to significant cost reductions.

Suggested Citation

  • Dekker, R. & Frenk, J.B.G. & Kleijn, M.J. & Piersma, N. & de Kok, T.G., 1995. "On the use of break quantities in multi--echelon distribution systems," Econometric Institute Research Papers EI 9548-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1361
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    References listed on IDEAS

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    1. George Tagaras & Morris A. Cohen, 1992. "Pooling in Two-Location Inventory Systems with Non-Negligible Replenishment Lead Times," Management Science, INFORMS, vol. 38(8), pages 1067-1083, August.
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    3. Lawrence D. Burns & Randolph W. Hall & Dennis E. Blumenfeld & Carlos F. Daganzo, 1985. "Distribution Strategies that Minimize Transportation and Inventory Costs," Operations Research, INFORMS, vol. 33(3), pages 469-490, June.
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    1. Dekker, R. & Kleijn, M. J. & de Kok, A. G., 1998. "The break quantity rule's effect on inventory costs in a 1-warehouse, N-retailers distribution system," International Journal of Production Economics, Elsevier, vol. 56(1), pages 61-68, September.
    2. Tempelmeier, Horst, 2006. "Supply chain inventory optimization with two customer classes in discrete time," European Journal of Operational Research, Elsevier, vol. 174(1), pages 600-621, October.
    3. Dekker, R. & Kleijn, M.J. & de Kok, A.G., 1996. "The break quantity rule in a 1-warehouse, N-retailers distribution system," Econometric Institute Research Papers EI 9624-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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