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A Fluid EOQ Model with Markovian Environment

Part of: Markov processes Special processes Operations 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: [email protected]
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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, reservoirs 60J28: Applications of continuous-time Markov processes on discrete state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 473 - 489
Copyright
© Applied Probability Trust 

References

Ahn, S. and Ramaswami, V. (2003). Fluid flow models and queues—a connection by stochastic coupling. Stoch. Models 19, 325–348.CrossRefGoogle Scholar
Ahn, S. and Ramaswami, V. (2005). Efficient algorithms for transient analysis of stochastic fluid flow models. J. Appl. Prob. 42, 531–549.CrossRefGoogle Scholar
Ahn, S. and Ramaswami, V. (2006). Transient analysis of fluid models via elementary level-crossing arguments. Stoch. Models 22, 129–147.CrossRefGoogle Scholar
Ahn, S., Badescu, A. L. and Ramaswami, V. (2007). Time dependent analysis of finite buffer fluid flows and risk models with a dividend barrier. Queueing Systems 55, 207–222.CrossRefGoogle Scholar
Asmussen, S. (2003). Applied Probability and Queues, 2nd edn. Springer, New York.Google Scholar
Asmussen, S. and Kella, O. (2000). A multi-dimensional martingale for Markov additive processes and its applications. Adv. Appl. Prob. 32, 376–393.CrossRefGoogle Scholar
Bean, N. G. and O'Reilly, M. M. (2008). Performance measure of a multi-layer Markovian fluid model. Ann. Operat. Res. 160, 99–120.CrossRefGoogle Scholar
Bean, N. G., O'Reilly, M. M. and Taylor, P. G. (2008). Algorithms for the Laplace–Stieltjes transforms of first return times for stochastic fluid flows. Methodol. Comput. Appl. Prob. 10, 381–408.CrossRefGoogle Scholar
Berman, O., Parlar, M., Perry, D. and Posner, M. J. M. (2005). Production/clearing models under continuous and sporadic review. Methodol. Comput. Appl. Prob. 7, 203–224.CrossRefGoogle Scholar
Berman, O. and Perry, D. (2006). An EOQ model with state-dependent demand rate. Europ. J. Operat. Res. 171, 255–272.CrossRefGoogle Scholar
Berman, O., Perry, D. and Stadje, W. (2006). A fluid EOQ model with a two-state random environment. Prob. Eng. Inf. Sci. 20, 329–349.CrossRefGoogle Scholar
Berman, O., Perry, D. and Stadje, W. (2008). Optimal replenishment in a Brownian motion EOQ model with hysteretic parameter changes. Internat. J. Inventory Res. 1, 1–19.CrossRefGoogle Scholar
Doob, J. L. (1953). Stochastic Processes. John Wiley, New York.Google Scholar
Kella, O., Perry, D. and Stadje, W. (2003). A stochastic clearing model with a Brownian and a compound Poisson component. Prob. Eng. Inf. Sci. 17, 1–22.CrossRefGoogle Scholar
Kulkarni, V. G. (2010). Modeling and Analysis of Stochastic Systems, 2nd edn. CRC Press, Boca Raton, FL.Google Scholar
Kulkarni, V. and Yan, K. (2007). A fluid model with upward Jumps at the boundary. Queueing Systems 56, 103–117.CrossRefGoogle Scholar
Nahmias, S. (1997). Production and Operations Analysis, 3rd edn. Irwin, Chicago, IL.Google Scholar
Perry, D., Berg, M. and Posner, M. J. M. (2001). Stochastic models for broker inventory in dealership markets with a cash management interpretation. Insurance Math. Econom. 29, 23–34.CrossRefGoogle Scholar
Perry, D., Stadje, W. and Zacks, S. (2005). Sporadic and continuous clearing policies for a production/inventory system under an M/G demand process. Math. Operat. Res. 30, 354–368.CrossRefGoogle Scholar
Ramaswami, M. V. (1999). Matrix analytic methods for stochastic fluid flows. Proceedings of the International Teletraffic Congress, ITC-16, Edinburgh, Elsevier, pp. 1019–1030.Google Scholar
Ramaswami, V. (2006). Passage times in fluid models with application to risk processes. Methodol. Comput. Appl. Prob. 8, 497–515.CrossRefGoogle Scholar
Ross, S. M. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.Google Scholar
Tzenova, E. I., Adan, I. J. B. F. and Kulkarni, V. G. (2005). Fluid models with Jumps. Stoch. Models 21, 37–55.CrossRefGoogle Scholar
Yan, K. and Kulkarni, V. G. (2008). Optimal inventory policies under stochastic production and demand rates. Stoch. Models 24, 173–190.CrossRefGoogle Scholar