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An Incomplete Information Inventory Model with Presence of Inventories or Backorders as Only Observations

Author

Listed:
  • A. Bensoussan

    (University of Texas at Dallas)

  • M. Çakanyıldırım

    (University of Texas at Dallas)

  • J. A. Minjárez-Sosa

    (Universidad de Sonora)

  • S. P. Sethi

    (University of Texas at Dallas)

  • R. Shi

    (University of Richmond)

Abstract

In many real-life contexts, inventory levels are only incompletely observed due to non-observation of demand, discrepancies in transmitting sales data, transaction errors, spoilage, misplacement, or theft of inventory. We study a periodic review inventory system, where the demand is not observed and the unmet demand is backordered. As a result, the inventory manager cannot tell the exact quantities of inventories or backorders. However, by looking at the shelf, he knows whether the inventory is positive or nonpositive. Only with this information, the inventory manager must determine the order quantity in each period that would minimize the expected total discounted cost over an infinite-horizon. The dynamic programming formulation of this problem has an infinite-dimensional state space. We use the concept of unnormalized probability to establish the existence of an optimal feedback policy and the uniqueness of the solution of the dynamic programming equation when the periodic cost has linear growth.

Suggested Citation

  • A. Bensoussan & M. Çakanyıldırım & J. A. Minjárez-Sosa & S. P. Sethi & R. Shi, 2010. "An Incomplete Information Inventory Model with Presence of Inventories or Backorders as Only Observations," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 544-580, September.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:3:d:10.1007_s10957-010-9678-1
    DOI: 10.1007/s10957-010-9678-1
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    Cited by:

    1. Eugene A. Feinberg & Pavlo O. Kasyanov & Michael Z. Zgurovsky, 2016. "Partially Observable Total-Cost Markov Decision Processes with Weakly Continuous Transition Probabilities," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 656-681, May.
    2. Rong Li & Jing‐Sheng Jeannette Song & Shuxiao Sun & Xiaona Zheng, 2022. "Fight inventory shrinkage: Simultaneous learning of inventory level and shrinkage rate," Production and Operations Management, Production and Operations Management Society, vol. 31(6), pages 2477-2491, June.

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