Finite Source Retrial Queue with Inventory Management: Semi MDP

Gowsalya, V., Selvakumar, C. and Elango, C.

Research Department of Mathematics, Cardamom Planters’ Association College, Bodinayakanur - 625 513, INDIA.

DOI : http://dx.doi.org/10.29055/jcms/1139


In this article, we address the problem of Ordering policy in retrial service facility system with inventory. We consider a finite source (N) demand generation system and unsatisfied demand enter an finite orbit for retrial. Arrival of demands to the system is assumed to follows a Poisson Process and service times are assumed to follows an exponential distribution. Let the maximum inventory S and (s,S) policy is adopted for replenishment. The system is formulated as Semi-Markov Decision Process and we find the controlling the inventory ordering policy implemented at each instant of time for a given inventory capacity S. Linear Programming method is implemented with the criterion minimizing the long-run expected cost rate. Numerical examples is provided to establish the result obtained.

Keywords :Inventory control, Service facility, Markov Decision Process, LPP and Policy iteration expect cost rate criteria.

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