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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
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Abstract

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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.

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 

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