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ON THE STRUCTURE OF OPTIMAL ORDERING POLICIES FOR STOCHASTIC INVENTORY SYSTEMS WITH MINIMUM ORDER QUANTITY

Published online by Cambridge University Press:  06 March 2006

Yao Zhao  and
Michael N. Katehakis
Yao Zhao
Affiliation:
Department of Management Science and Information Systems, Rutgers University, The State University of New Jersey, Newark, NJ 07102-1895, E-mail: yaozhao@andromeda.rutgers.edu
Michael N. Katehakis
Affiliation:
Department of Management Science and Information Systems, Rutgers University, The State University of New Jersey, Newark, NJ 07102-1895, E-mail: mnk@andromeda.rutgers.edu
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Abstract

We study a single-product periodic-review inventory model in which the ordering quantity is either zero or at least a minimum order size. The ordering cost is a linear function of the ordering quantity, and the demand in different time periods are independent random variables. The objective is to characterize the inventory policies that minimize the total discounted ordering, holding, and backorder penalty costs over a finite time horizon. We introduce the concept of an M-increasing function. These functions allow us to characterize the optimal inventory policies everywhere in the state space outside of an interval for each time period. Furthermore, we identify easily computable upper bounds and asymptotic lower bounds for these intervals. Finally, examples are given to demonstrate the complex structure of the optimal inventory policies.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 2 , April 2006 , pp. 257 - 270
Copyright
© 2006 Cambridge University Press

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