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A Fluid EOQ Model with Markovian Environment

Part of:Special processesMarkov processesOperations research and management science

Published online by Cambridge University Press:  30 January 2018

Yonit Barron
Yonit Barron*
Affiliation:
Ariel University
*
∗ Postal address: Department of Industrial Engineering and Management, Ariel University, Ariel, 40700, Israel. Email address: ybarron@ariel.ac.il
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Abstract

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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.

Keywords

Production-inventory modelbacklogcost functionalfluid flow processmartingaleEOQ

MSC classification

Primary:60K10: Applications (reliability, demand theory, etc.)
Secondary:90B05: Inventory, storage, reservoirs60J28: Applications of continuous-time Markov processes on discrete state spaces

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015, pp. 473 - 489
Copyright
© Applied Probability Trust 

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