A JUMP-FLUID PRODUCTION–INVENTORY MODEL WITH A DOUBLE BAND CONTROL. Issue 3 (15th April 2014)

• Record Type: Journal Article
• Authors: Barron, Yonit; Perry, David; Stadje, Wolfgang
• Is Part Of: Probability in the engineering and informational sciences. Volume 28:Issue 3(2014)
• Page Start: 313
• Page End: 333
• Publication Date: 2014-04-15
• Subjects: Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964814000023
• Languages: English
• ISSNs: 0269-9648

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>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.</p> </abstract>