Journal of Applied Probability

A fluid EOQ model with Markovian environment

Yonit Barron

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We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

Article information

J. Appl. Probab., Volume 52, Number 2 (2015), 473-489.

First available in Project Euclid: 23 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 90B05: Inventory, storage, reservoirs 60J28: Applications of continuous-time Markov processes on discrete state spaces

Production-inventory model backlog cost functional fluid flow process martingale EOQ


Barron, Yonit. A fluid EOQ model with Markovian environment. J. Appl. Probab. 52 (2015), no. 2, 473--489. doi:10.1239/jap/1437658610.

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