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Balancing Retailer Inventories

Author

Listed:
  • Edward J. McGavin

    (KPMG Peat Marwick LLP, Chicago, Illinois)

  • James E. Ward

    (Purdue University, West Lafayette, Indiana)

  • Leroy B. Schwarz

    (Purdue University, West Lafayette, Indiana)

Abstract

This paper examines the optimality of inventory “balancing” in a one-warehouse N -retailer distribution system facing stochastic demand for a single product over T successive time intervals. In particular, we consider the division of predetermined quantities of warehouse stock among retailers in each interval. Balancing attempts to bring the retailer-inventories to the same (normalized with respect to first-interval demand) net inventory level. When the demand distribution over the T periods is symmetric with respect to all pairs of retailers, and retailer cost over the T -intervals is a convex function of the T shipments, we show that balancing divisions are optimal. The required convexity condition is shown to be satisfied for some familiar cost functions when shortages are backordered and lost. However for other cost functions, the convexity condition is satisfied under backordering, but not under lost sales. We also consider the nonidentical-retailer (demands are not symmetric) case and provide examples to show that balancing is generally not optimal, even for relatively common, simple cost functions.

Suggested Citation

  • Edward J. McGavin & James E. Ward & Leroy B. Schwarz, 1997. "Balancing Retailer Inventories," Operations Research, INFORMS, vol. 45(6), pages 820-830, December.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:6:p:820-830
    DOI: 10.1287/opre.45.6.820
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    Citations

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    Cited by:

    1. Assaf Avrahami & Yale T. Herer & Retsef Levi, 2014. "Matching Supply and Demand: Delayed Two-Phase Distribution at Yedioth Group—Models, Algorithms, and Information Technology," Interfaces, INFORMS, vol. 44(5), pages 445-460, October.
    2. Ankur Goel & Genaro J. Gutierrez, 2011. "Multiechelon Procurement and Distribution Policies for Traded Commodities," Management Science, INFORMS, vol. 57(12), pages 2228-2244, December.
    3. Sven Axsäter & Johan Marklund & Edward A. Silver, 2002. "Heuristic Methods for Centralized Control of One-Warehouse, N-Retailer Inventory Systems," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 75-97, October.
    4. Seifert, Ralf W. & Tancrez, Jean-Sébastien & Biçer, Işık, 2016. "Dynamic product portfolio management with life cycle considerations," International Journal of Production Economics, Elsevier, vol. 171(P1), pages 71-83.
    5. Qinan Wang & Sven Axsäter, 2013. "Fixed‐interval joint‐replenishment policies for distribution systems with multiple retailers and stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 637-651, December.
    6. Stephen A. Smith & Narendra Agrawal, 2000. "Management of Multi-Item Retail Inventory Systems with Demand Substitution," Operations Research, INFORMS, vol. 48(1), pages 50-64, February.
    7. Seifert, Ralf W. & Thonemann, Ulrich W. & Sieke, Marcel A., 2006. "Integrating direct and indirect sales channels under decentralized decision-making," International Journal of Production Economics, Elsevier, vol. 103(1), pages 209-229, September.
    8. Agrawal, Vipul & Chao, Xiuli & Seshadri, Sridhar, 2004. "Dynamic balancing of inventory in supply chains," European Journal of Operational Research, Elsevier, vol. 159(2), pages 296-317, December.
    9. Sasanuma, Katsunobu & Hibiki, Akira & Sexton, Thomas, 2022. "An opaque selling scheme to reduce shortage and wastage in perishable inventory systems," Operations Research Perspectives, Elsevier, vol. 9(C).
    10. Wang, Qinan, 2013. "A periodic-review inventory control policy for a two-level supply chain with multiple retailers and stochastic demand," European Journal of Operational Research, Elsevier, vol. 230(1), pages 53-62.
    11. Johan Marklund & Kaj Rosling, 2012. "Lower Bounds and Heuristics for Supply Chain Stock Allocation," Operations Research, INFORMS, vol. 60(1), pages 92-105, February.
    12. Mila Nambiar & David Simchi‐Levi & He Wang, 2021. "Dynamic Inventory Allocation with Demand Learning for Seasonal Goods," Production and Operations Management, Production and Operations Management Society, vol. 30(3), pages 750-765, March.

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