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

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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.

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Authors and Affiliations

  1. School of Management, University of Texas at Dallas, Richardson, TX, USA

    A. Bensoussan, M. Çakanyıldırım & S. P. Sethi

  2. Departamento de Matemáticas, Universidad de Sonora, Hermosillo, Sonora, Mexico

    J. A. Minjárez-Sosa

  3. Robins School of Business, University of Richmond, Richmond, VA, USA

    R. Shi

Authors
  1. A. Bensoussan
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  2. M. Çakanyıldırım
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  3. J. A. Minjárez-Sosa
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  4. S. P. Sethi
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  5. R. Shi
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Corresponding author

Correspondence to S. P. Sethi.

Additional information

Communicated by G. Leitmann.

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Bensoussan, A., Çakanyıldırım, M., Minjárez-Sosa, J.A. et al. An Incomplete Information Inventory Model with Presence of Inventories or Backorders as Only Observations. J Optim Theory Appl 146, 544–580 (2010). https://doi.org/10.1007/s10957-010-9678-1

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  • DOI: https://doi.org/10.1007/s10957-010-9678-1

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