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Single-item continuous-review inventory models with random supplies

Part of: Operations research and management science Stochastic systems and control Stochastic analysis

Published online by Cambridge University Press:  27 January 2025

Kurt L. Helmes ,
Richard H. Stockbridge  and
Chao Zhu Open the ORCID record for Chao Zhu [Opens in a new window]
Kurt L. Helmes*
Affiliation:
Humboldt University of Berlin
Richard H. Stockbridge*
Affiliation:
University of Wisconsin–Milwaukee
Chao Zhu*
Affiliation:
University of Wisconsin–Milwaukee
*
*Postal address: Institute for Operations Research, Humboldt University of Berlin, Spandauer Str. 1, 10178, Berlin, Germany. Email address: [email protected]
**Postal address: Department of Mathematical Sciences, University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA.
**Postal address: Department of Mathematical Sciences, University of Wisconsin–Milwaukee, Milwaukee, WI 53201, USA.
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Abstract

This paper analyzes single-item continuous-review inventory models with random supplies in which the inventory dynamic between orders is described by a diffusion process, and a long-term average cost criterion is used to evaluate decisions. The models in this class have general drift and diffusion coefficients and boundary points that are consistent with the notion that demand should tend to reduce the inventory level. Random yield is described by a (probability) transition function which depends on the inventory on hand and the nominal amount ordered; it is assumed to be a distribution with support in the interval determined by the order-from and the nominal order-to locations of the stock level. Using weak convergence arguments involving average expected occupation and ordering measures, conditions are given for the optimality of an (s, S) ordering policy in the general class of policies with finite expected cost. The characterization of the cost of an (s, S) policy as a function of two variables naturally leads to a nonlinear optimization problem over the stock levels s and S, and the existence of an optimizing pair $(s^*,S^*)$ is established under weak conditions. Thus, optimal policies of inventory models with random supplies can (easily) be numerically computed. The range of applicability of the optimality result is illustrated on several inventory models with random yields.

Keywords

Inventory models with random suppliesimpulse controllong-term average costgeneral diffusion models(s, S) policiesweak convergence

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 90B05: Inventory, storage, reservoirs 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 37
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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