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Conditions that cause risk pooling to increase inventory


  • Yang, Hongsuk
  • Schrage, Linus


We say product A is a partial substitute for product B if a fraction of the customers who prefer B are willing to accept A when B is out of stock. When demand is uncertain, it is intuitive and true that a larger "willing to substitute" fraction implies larger expected profits. A higher "willing to substitute" fraction allows one to pool the risk of individual products. It may also be intuitive that a larger "willing to substitute" fraction might result in lower optimal total inventory. For the full substitution structure, several researchers have shown that for certain distributions such as the exponential, this latter intuition is not true. We show that this full substitution anomaly can occur with any right skewed demand distribution. We assume i.i.d. demand distributions unless we indicate otherwise. We also show that the anomaly can occur for a number of realistic situations of partial substitution with commonly used demand distributions such as Normal, exponential, Poisson, and uniform. We also demonstrate the anomaly for more than one period, with backlogging, lost sales, more than two products, and with setup costs.

Suggested Citation

  • Yang, Hongsuk & Schrage, Linus, 2009. "Conditions that cause risk pooling to increase inventory," European Journal of Operational Research, Elsevier, vol. 192(3), pages 837-851, February.
  • Handle: RePEc:eee:ejores:v:192:y:2009:i:3:p:837-851

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    References listed on IDEAS

    1. Ravi Anupindi & Maqbool Dada & Sachin Gupta, 1998. "Estimation of Consumer Demand with Stock-Out Based Substitution: An Application to Vending Machine Products," Marketing Science, INFORMS, vol. 17(4), pages 406-423.
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    7. Ricardo Ernst & Panagiotis Kouvelis, 1999. "The Effects of Selling Packaged Goods on Inventory Decisions," Management Science, INFORMS, vol. 45(8), pages 1142-1155, August.
    8. Ravi Anupindi & Yehuda Bassok, 1999. "Centralization of Stocks: Retailers vs. Manufacturer," Management Science, INFORMS, vol. 45(2), pages 178-191, February.
    9. Jovan Grahovac & Amiya Chakravarty, 2001. "Sharing and Lateral Transshipment of Inventory in a Supply Chain with Expensive Low-Demand Items," Management Science, INFORMS, vol. 47(4), pages 579-594, April.
    10. Gerchak, Yigal & Wang, Shaun, 1997. "Liquid asset allocation using "newsvendor" models with convex shortage costs," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 17-21, June.
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    Cited by:

    1. Sahba, Pedram & BalcIog[small tilde]lu, BarIs, 2011. "The impact of transportation delays on repairshop capacity pooling and spare part inventories," European Journal of Operational Research, Elsevier, vol. 214(3), pages 674-682, November.
    2. Çömez-Dolgan, Nagihan & Tanyeri, Başak, 2015. "Inventory performance with pooling: Evidence from mergers and acquisitions," International Journal of Production Economics, Elsevier, vol. 168(C), pages 331-339.
    3. Shin, Hojung & Park, Soohoon & Lee, Euncheol & Benton, W.C., 2015. "A classification of the literature on the planning of substitutable products," European Journal of Operational Research, Elsevier, vol. 246(3), pages 686-699.
    4. Smirnov, Dina & Gerchak, Yigal, 2016. "Inventory sharing via circular bidirectional chaining," International Journal of Production Economics, Elsevier, vol. 179(C), pages 141-152.
    5. Edirisinghe, Chanaka & Atkins, Derek, 2017. "Lower bounding inventory allocations for risk pooling in two-echelon supply chains," International Journal of Production Economics, Elsevier, vol. 187(C), pages 159-167.
    6. H. Mirzaei, Fouad & Ødegaard, Fredrik & Yan, Xinghao, 2015. "User reward programs in online social media," Omega, Elsevier, vol. 57(PB), pages 123-144.
    7. Nagihan Çömez & Kathryn E. Stecke & Metin Çakanyildirim, 2012. "In-Season Transshipments Among Competitive Retailers," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 290-300, April.
    8. Eda Kemahl{i}ou{g}lu-Ziya & John J. Bartholdi, III, 2011. "Centralizing Inventory in Supply Chains by Using Shapley Value to Allocate the Profits," Manufacturing & Service Operations Management, INFORMS, vol. 13(2), pages 146-162, September.
    9. Schmitt, Amanda J. & Sun, Siyuan Anthony & Snyder, Lawrence V. & Shen, Zuo-Jun Max, 2015. "Centralization versus decentralization: Risk pooling, risk diversification, and supply chain disruptions," Omega, Elsevier, vol. 52(C), pages 201-212.
    10. Smirnov, Dina & Gerchak, Yigal, 2014. "Inventory sharing via circular unidirectional chaining," European Journal of Operational Research, Elsevier, vol. 237(2), pages 474-486.
    11. repec:eee:ejores:v:263:y:2017:i:2:p:479-492 is not listed on IDEAS
    12. Huang, Di & Zhou, Hong & Zhao, Qiu-Hong, 2011. "A competitive multiple-product newsboy problem with partial product substitution," Omega, Elsevier, vol. 39(3), pages 302-312, June.


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