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Newsvendor Bounds and Heuristic for Optimal Policies in Serial Supply Chains


  • Kevin H. Shang

    () (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Jing-Sheng Song

    () (Graduate School of Management, University of California, Irvine, California 92697)


We consider the classic N-stage serial supply systems with linear costs and stationary random demands. There are deterministic transportation leadtimes between stages, and unsatisfied demands are backlogged. The optimal inventory policy for this system is known to be an echelon base-stock policy, which can be computed through minimizing N nested convex functions recursively. To identify the key determinants of the optimal policy, we develop a simple and surprisingly good heuristic. This method minimizes 2Nseparate newsvendor-type cost functions, each of which uses the original problem data only. These functions are lower and upper bounds for the echelon cost functions; their minimizers form bounds for the optimal echelon base-stock levels. The heuristic is the simple average of the solution bounds. In extensive numerical experiments, the average relative error of the heuristic is 0.24%, with the maximum error less than 1.5%. The bounds and the heuristic, which can be easily obtained by simple spreadsheet calculations, enhance the accessibility and implementability of the multiechelon inventory theory. More importantly, the closed-form expressions provide an analytical tool for us to gain insights into issues such as system bottlenecks, effects of system parameters, and coordination mechanisms in decentralized systems.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormnsc:v:49:y:2003:i:5:p:618-638

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    References listed on IDEAS

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    1. repec:eee:proeco:v:196:y:2018:i:c:p:188-197 is not listed on IDEAS
    2. Kevin H. Shang & Jing-Sheng Song, 2006. "A Closed-Form Approximation for Serial Inventory Systems and Its Application to System Design," Manufacturing & Service Operations Management, INFORMS, vol. 8(4), pages 394-406, September.
    3. Hsieh, Chung-Chi & Wu, Cheng-Han & Huang, Ya-Jing, 2008. "Ordering and pricing decisions in a two-echelon supply chain with asymmetric demand information," European Journal of Operational Research, Elsevier, vol. 190(2), pages 509-525, October.
    4. Sari, Kazim, 2008. "On the benefits of CPFR and VMI: A comparative simulation study," International Journal of Production Economics, Elsevier, vol. 113(2), pages 575-586, June.
    5. Gérard P. Cachon & A. Gürhan Kök, 2007. "Implementation of the Newsvendor Model with Clearance Pricing: How to (and How Not to) Estimate a Salvage Value," Manufacturing & Service Operations Management, INFORMS, vol. 9(3), pages 276-290, October.
    6. Noel Watson & Yu-Sheng Zheng, 2005. "Decentralized Serial Supply Chains Subject to Order Delays and Information Distortion: Exploiting Real-Time Sales Data," Manufacturing & Service Operations Management, INFORMS, vol. 7(2), pages 152-168, May.
    7. Albrecht, Martin, 2014. "Determining near optimal base-stock levels in two-stage general inventory systems," European Journal of Operational Research, Elsevier, vol. 232(2), pages 342-349.
    8. Buchheit, Steve & Feltovich, Nick, 2010. "Experimental evidence of a sunk–cost paradox: a study of pricing behavior in Bertrand–Edgeworth duopoly," SIRE Discussion Papers 2010-124, Scottish Institute for Research in Economics (SIRE).
    9. Diwakar Gupta & N. Selvaraju, 2006. "Performance Evaluation and Stock Allocation in Capacitated Serial Supply Systems," Manufacturing & Service Operations Management, INFORMS, vol. 8(2), pages 169-191, July.
    10. Saibal Ray & Shanling Li & Yuyue Song, 2005. "Tailored Supply Chain Decision Making Under Price-Sensitive Stochastic Demand and Delivery Uncertainty," Management Science, INFORMS, vol. 51(12), pages 1873-1891, December.
    11. 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.
    12. Kevin H. Shang, 2012. "Single-Stage Approximations for Optimal Policies in Serial Inventory Systems with Nonstationary Demand," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 414-422, July.


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