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

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

6 Scopus Citations
View graph of relations

Author(s)

  • A. Bensoussan
  • M. Çakanyildirim
  • J. A. Minjárez-Sosa
  • S. P. Sethi
  • R. Shi

Detail(s)

Original languageEnglish
Pages (from-to)544-580
Journal / PublicationJournal of Optimization Theory and Applications
Volume146
Issue number3
Publication statusPublished - 2010
Externally publishedYes

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. © 2010 Springer Science+Business Media, LLC.

Research Area(s)

  • Backordered unmet demand, Positive-inventory signal, Unobserved inventory level

Citation Format(s)

An Incomplete Information Inventory Model with Presence of Inventories or Backorders as Only Observations. / Bensoussan, A.; Çakanyildirim, M.; Minjárez-Sosa, J. A. et al.
In: Journal of Optimization Theory and Applications, Vol. 146, No. 3, 2010, p. 544-580.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review