Journal
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
Volume 85, Issue 4, Pages 589-603Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17442508.2013.802091
Keywords
existence; uniqueness; demand; shrinkage; inventory
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Funding
- World Class University (WCU) programme through the National Research Foundation of Korea
- Ministry of Education, Science and Technology [R31 - 20007]
- Research Grants Council of the Hong Kong Special Administrative Region [CityU 500111]
- University of Texas at Dallas
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We study a discrete-time periodic-review inventory system where the unmet demand is lost, and the excess inventory is subject to shrinkage. We first derive the state evolution and then introduce unnormalized conditional probabilities to transform the nonlinear state evolution into a linear one. We then prove the existence and uniqueness of the solution for the Bellman equation in the case of unbounded costs and show that the solution yields the value function.
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