TY - JOUR
T1 - A jump-fluid production-inventory model with a double band control
AU - Barron, Yonit
AU - Perry, David
AU - Stadje, Wolfgang
PY - 2014/7
Y1 - 2014/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84902269839&partnerID=8YFLogxK
U2 - 10.1017/S0269964814000023
DO - 10.1017/S0269964814000023
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AN - SCOPUS:84902269839
SN - 0269-9648
VL - 28
SP - 313
EP - 333
JO - Probability in the Engineering and Informational Sciences
JF - Probability in the Engineering and Informational Sciences
IS - 3
ER -