Hostname: page-component-89b8bd64d-b5k59 Total loading time: 0 Render date: 2026-05-06T23:26:04.433Z Has data issue: false hasContentIssue false
  • English
  • Français

A JUMP-FLUID PRODUCTION–INVENTORY MODEL WITH A DOUBLE BAND CONTROL

Published online by Cambridge University Press:  15 April 2014

Yonit Barron ,
David Perry  and
Wolfgang Stadje
Yonit Barron
Affiliation:
Department of Statistics, University of Haifa, Haifa 91905, Israel Email: ybarron@stat.haifa.ac.il
David Perry
Affiliation:
Department of Statistics, University of Haifa, Haifa 91905, Israel Email: dperry@stat.haifa.ac.il
Wolfgang Stadje
Affiliation:
Institute of Mathematics, University of Osnabrück, 49069 Osnabrück, Germany Email: wstadje@uos.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We consider a production–inventory control model with two reflecting boundaries, representing the finite storage capacity and the finite maximum backlog. Demands arrive at the inventory according to a Poisson process, their i.i.d. sizes having a common phase-type distribution. The inventory is filled by a production process, which alternates between two prespecified production rates ρ1 and ρ2: as long as the content level is positive, ρ1 is applied while the production follows ρ2 during time intervals of backlog (i.e., negative content). We derive in closed form the various cost functionals of this model for the discounted case as well as under the long-run-average criterion. The analysis is based on a martingale of the Kella–Whitt type and results for fluid flow models due to Ahn and Ramaswami.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 3 , July 2014 , pp. 313 - 333
Copyright
Copyright © Cambridge University Press 2014 

References

1.Ahn, S. & Ramaswami, V. (2004). Transient analysis of fluid flow Models via stochastic coupling to a queue. Stochastic Models 20: 71–101.CrossRefGoogle Scholar
2.Ahn, S. & Ramaswami, V. (2005). Efficient algorithms for transient analysis of stochastic fluid flow models. Journal of Applied Probability 42: 531–549.Google Scholar
3.Ahn, S. & Ramaswami, V. (2006). Transient analysis of fluid models via elementary level-crossing arguments. Stochastic Models 22: 129–147.Google Scholar
4.Ahn, S., Badescu, A.L. & 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
5.Baek, J.W., Lee, H.W., Lee, S.W. & Ahn, S. (2011). A Markov modulated fluid flow queueing model under D-policy. Numerical Linear Algebra with Applications 18: 993–1010.Google Scholar
6.Boxma, O.J., Perry, D. & Stadje, W. (2001). Clearing models for M/G/1 queues. Queueing Systems 38: 287–306.Google Scholar
7.Dickson, D.C.M. & Waters, H.R. (2004). Some optimal dividends problems. ASTIN Bulletin 34: 49–74.CrossRefGoogle Scholar
8.Doshi, B.T., Van Der Duyn Schouten, F.A. & Talman, J.J. (1978). A Production inventory control model with a mixture of back-orders and lost-sales. Management Science 24: 1078–1087.Google Scholar
9.Kella, O. & Whitt, W. (1992). Useful martingales for stochastic storage processes with Lévy input. Journal of Applied Probability 29: 396–403.Google Scholar
10.Kella, O., Perry, D. & Stadje, W. (2003). A stochastic clearing model with Brownian and a compound Poisson component. Probability in the Engineering and Informational Sciences 17: 1–22.CrossRefGoogle Scholar
11.Kulkarni, V.G. & Yan, K. (2007). A fluid model with upward jumps at the boundary. Queueing Systems 56: 103–117.CrossRefGoogle Scholar
12.Kulkarni, V.G. & Yan, K. (2012). Production-inventory systems in stochastic environment and stochastic lead times. Queueing Systems 70: 207–231.Google Scholar
13.Perry, D., Berg, M. & Posner, M.J.M. (2001). Stochastic models for broker inventory in dealership markets with a cash management interpretation. Insurance: Mathematics and Economics 29: 23–34.Google Scholar
14.Perry, D., Stadje, W. & Zacks, S. (2005). Sporadic and continuous clearing policies for a production/inventory system under an M/G demand process. Mathematics of Operations Research 30: 354–368.Google Scholar
15.Ramaswami, V. (2006). Passage times in fluid models with application to risk processes. Methodology and Computing in Applied Probability 8: 497–515.Google Scholar
16.Yan, K. & Kulkarni, V.G. (2008). Optimal inventory policies under stochastic production and demand rates. Stochastic Models 24: 173–190.Google Scholar