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Analysis of a two-echelon inventory system with two supply modes


  • Arts, Joachim
  • Kiesmüller, Gudrun P.


In this paper, we consider a serial two-echelon periodic review inventory system with two supply modes at the most upstream stock point. As control policy for this system, we propose a natural extension of the dual-index policy, which has three base-stock levels. We consider the minimization of long run average inventory holding, backlogging, and both per unit and fixed emergency ordering costs. We provide nested newsboy characterizations for two of the three base-stock levels involved and show a separability result for the difference with the remaining base-stock level. We extend results for the single-echelon system to efficiently approximate the distributions of random variables involved in the newsboy equations and find an asymptotically correct approximation for both the per unit and fixed emergency ordering costs. Based on these results, we provide an algorithm for setting base-stock levels in a computationally efficient manner. In a numerical study, we investigate the value of dual-sourcing in supply chains and illustrate that dual-sourcing can lead to significant cost savings in cases with high demand uncertainty, high backlogging cost or long lead times.

Suggested Citation

  • Arts, Joachim & Kiesmüller, Gudrun P., 2013. "Analysis of a two-echelon inventory system with two supply modes," European Journal of Operational Research, Elsevier, vol. 225(2), pages 263-272.
  • Handle: RePEc:eee:ejores:v:225:y:2013:i:2:p:263-272
    DOI: 10.1016/j.ejor.2012.09.043

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    References listed on IDEAS

    1. Kevin H. Shang & Jing-Sheng Song, 2003. "Newsvendor Bounds and Heuristic for Optimal Policies in Serial Supply Chains," Management Science, INFORMS, vol. 49(5), pages 618-638, May.
    2. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    3. Minner, Stefan, 2003. "Multiple-supplier inventory models in supply chain management: A review," International Journal of Production Economics, Elsevier, vol. 81(1), pages 265-279, January.
    4. Gad Allon & Jan A. Van Mieghem, 2010. "Global Dual Sourcing: Tailored Base-Surge Allocation to Near- and Offshore Production," Management Science, INFORMS, vol. 56(1), pages 110-124, January.
    5. Fangruo Chen & Yu-Sheng Zheng, 1994. "Lower Bounds for Multi-Echelon Stochastic Inventory Systems," Management Science, INFORMS, vol. 40(11), pages 1426-1443, November.
    6. Xu, Ningxiong, 2009. "Optimal policy for a two-facility inventory problem with storage constraints and two freight modes," European Journal of Operational Research, Elsevier, vol. 194(1), pages 78-84, April.
    7. Yoichiro Fukuda, 1964. "Optimal Policies for the Inventory Problem with Negotiable Leadtime," Management Science, INFORMS, vol. 10(4), pages 690-708, July.
    8. Janssen, Fred & de Kok, Ton, 1999. "A two-supplier inventory model," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 395-403, March.
    9. Jing-Sheng Song & Paul Zipkin, 2009. "Inventories with Multiple Supply Sources and Networks of Queues with Overflow Bypasses," Management Science, INFORMS, vol. 55(3), pages 362-372, March.
    10. Klosterhalfen, Steffen & Kiesmüller, Gudrun & Minner, Stefan, 2011. "A comparison of the constant-order and dual-index policy for dual sourcing," International Journal of Production Economics, Elsevier, vol. 133(1), pages 302-311, September.
    11. Chiang, Chi, 2007. "Optimal control policy for a standing order inventory system," European Journal of Operational Research, Elsevier, vol. 182(2), pages 695-703, October.
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    Cited by:

    1. Song, Dong-Ping & Dong, Jing-Xin & Xu, Jingjing, 2014. "Integrated inventory management and supplier base reduction in a supply chain with multiple uncertainties," European Journal of Operational Research, Elsevier, vol. 232(3), pages 522-536.
    2. repec:eee:ejores:v:267:y:2018:i:1:p:150-161 is not listed on IDEAS
    3. repec:eee:ejores:v:264:y:2018:i:1:p:89-105 is not listed on IDEAS


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