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A Periodic-Review Base-Stock Inventory System with Sales Rejection

Author

Listed:
  • Yanyi Xu

    (School of Management, Shanghai University, Shanghai 200444, China)

  • Arnab Bisi

    (Krannert School of Management, Purdue University, West Lafayette, Indiana 47907)

  • Maqbool Dada

    (The Johns Hopkins Carey Business School, Baltimore, Maryland 21201)

Abstract

We consider a system in which an order is placed every T periods to bring the inventory position up to the base stock S . We accept demand until the inventory position reaches a sales rejection threshold M . Our objective is to find the optimal values of S and M that minimize the long-run average cost per period. We establish the stationary distribution of our system and develop structural properties of the optimal solution that facilitate computation. In particular, we show that in an optimal solution, the optimal value of M is nonnegative under some reasonable conditions. Hence, in our model a mixture of backorders and lost sales may occur. Additionally, we compare our system against traditional systems in which demand during stockouts is either fully backordered or lost.

Suggested Citation

  • Yanyi Xu & Arnab Bisi & Maqbool Dada, 2011. "A Periodic-Review Base-Stock Inventory System with Sales Rejection," Operations Research, INFORMS, vol. 59(3), pages 742-753, June.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:3:p:742-753
    DOI: 10.1287/opre.1110.0921
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    References listed on IDEAS

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    1. T. W. Archibald & S. A. E. Sassen & L. C. Thomas, 1997. "An Optimal Policy for a Two Depot Inventory Problem with Stock Transfer," Management Science, INFORMS, vol. 43(2), pages 173-183, February.
    2. Yanyi Xu & Arnab Bisi & Maqbool Dada, 2010. "A centralized ordering and allocation system with backorders and strategic lost sales," IISE Transactions, Taylor & Francis Journals, vol. 42(11), pages 812-824.
    3. Chen, Fangruo & Zheng, Yu-Sheng, 1993. "Inventory models with general backorder costs," European Journal of Operational Research, Elsevier, vol. 65(2), pages 175-186, March.
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    6. Hemant K. Bhargava & Daewon Sun & Susan H. Xu, 2006. "Stockout Compensation: Joint Inventory and Price Optimization in Electronic Retailing," INFORMS Journal on Computing, INFORMS, vol. 18(2), pages 255-266, May.
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    Cited by:

    1. Adam N. Elmachtoub & Retsef Levi, 2016. "Supply Chain Management with Online Customer Selection," Operations Research, INFORMS, vol. 64(2), pages 458-473, April.
    2. Marco Bijvank & Woonghee Tim Huh & Ganesh Janakiraman & Wanmo Kang, 2014. "Robustness of Order-Up-to Policies in Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 62(5), pages 1040-1047, October.
    3. Yanyi Xu & Doğan A. Serel & Arnab Bisi & Maqbool Dada, 2022. "Coping with Demand Uncertainty: The Interplay between Dual Sourcing and Endogenous Partial Backordering," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1560-1575, April.
    4. Sreekumar Bhaskaran & Karthik Ramachandran & John Semple, 2010. "A Dynamic Inventory Model with the Right of Refusal," Management Science, INFORMS, vol. 56(12), pages 2265-2281, December.

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