Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2025-01-01T08:19:10.736Z Has data issue: false hasContentIssue false
  • English
  • Français

A FLUID EOQ MODEL WITH A TWO-STATE RANDOM ENVIRONMENT

Published online by Cambridge University Press:  06 March 2006

Oded Berman ,
David Perry  and
Wolfgang Stadje
Oded Berman
Affiliation:
Rotman School of Management, University of Toronto, Toronto, Canada, E-mail: Berman@rotman.utoronto.ca
David Perry
Affiliation:
Department of Statistics, University of Haifa, Haifa, Israel, E-mail: dperry@stat.haifa.ac.il
Wolfgang Stadje
Affiliation:
Department of Mathematics and Computer Science, University of Osnabrück, Osnabrück, Germany, E-mail: wolfgang@mathematik.uni-osnabrueck.de
Get access Rights & Permissions [Opens in a new window]

Abstract

We study a stochastic fluid EOQ-type model operating in a Markovian random environment of alternating good and bad periods determining the demand rate. We deal with the classical problem of “when to place an order” and “how big it should be,” leading to the trade-off between the setup cost and the holding cost. The key functionals are the steady-state mean of the content level, the expected cycle length (which is the time between two large orders), and the expected number of orders in a cycle. These performance measures are derived in closed form by using the level crossing approach in an intricate way. We also present numerical examples and carry out a sensitivity analysis.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 2 , April 2006 , pp. 329 - 349
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Asmussen, S. (2003). Applied probability and queues, 2nd ed. New York: Springer-Verlag.
Bar-Lev, S.K., Parlar, M., & Perry, D. (1994). On the EOQ model with inventory-level-dependent demand rate and random yield. Operations Research Letters 16: 167–176.Google Scholar
Berman, O., Krass, D., & Perry, D. (2003). A transfer/clearing inventory model under sporadic review. Mathematical Methods of Operations Research 57: 329–344.Google Scholar
Berman, O. & Perry, D. (2001). Two control policies for stochastic EOQ-type models. Probability in the Engineering and Informational Sciences 15: 445–463.Google Scholar
Berman, O. & Perry, D. (2006). An EOQ model with state-dependent demand rate. European Journal of Operational Research 171: 255–272.Google Scholar
Berman, O., Perry, D., & Stadje, W. (2004). Jump/fluid EOQ models with random yield and state-dependent input and output (submitted).
Cohen, J.W. (1977). On up and down crossings. Journal of Applied Probability 14: 405–410.Google Scholar
David, I. & Greenshteyn, E. (1997). Brownian analysis of a buffered-flow system in the face of sudden obsolescence. Operations Research Letters 19: 43–49.Google Scholar
Doshi, B.T. (1992). Level crossing analysis of queues. In U.N. Bhat & I.V. Basawa (eds.), Queueing and related models. Oxford: Clarendon Press, pp. 3–33.
Gerchak, Y. & Parlar, M. (1989). Control of a production system with variable yield and random demand. Computers and Operations Research 14: 315–324.Google Scholar
Gerchak, Y. & Parlar, M. (1990). Yield randomness, cost tradeoffs and diversification in the EOQ model. Naval Research Logistics 37: 341–354.Google Scholar
Kella, O. & Whitt, W. (1992). Useful martingales for storage systems with Lévy input. Journal of Applied Probability 29: 396–493.Google Scholar
Liu, L. (1990). (s,S) Continuous review models for inventory with random lifetime. Operations Research Letters 9: 161–167.Google Scholar
Liu, L. & Yang, T. (1999). An (s,S) random lifetime inventory model with a positive lead time. European Journal of Operations Research 113: 52–63.Google Scholar
Nahmias, S. (1997). Production and operations analysis, 3rd ed. New York: Irwin/McGraw-Hill.
Ross, S.M. (1996). Stochastic processes, 2nd ed. New York: Wiley.
Zipkin, P.H. (2000). Foundations of inventory management. New York: McGraw-Hill.