Optimal inventory control with shrinkage and observed sales

Abstract

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.

Keywords:

• existence
• uniqueness
• demand
• shrinkage
• inventory

Keywords:

• 90B05
• 93E20
• 93C41

Acknowledgements

This research was supported by World Class University (WCU) programme through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (R31 – 20007), and by the Research Grants Council of the Hong Kong Special Administrative Region (CityU 500111) and University of Texas at Dallas.