A jump-fluid production-inventory model with a double band control

Yonit Barron, David Perry, Wolfgang Stadje

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)313-333
Number of pages21
JournalProbability in the Engineering and Informational Sciences
Issue number3
StatePublished - Jul 2014
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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