An inventory system with Markovian demands, phase type distributions for perishability and replenishment
In this paper we consider a version of (s, S)-type inventory system in which the demands occur according to a Markovian arrival process (MAP). The shelf life times of the items in the inventory as well as the replenishment times are assumed to be of (possibly different) phase type. Demands that are not met immediately are stored in an unmet buffer of finite capacity. Any arriving demand finding the inventory level at zero and the unmet buffer to be full is considered lost. Demands in the unmet buffer compete for the inventory after waiting for a random amount of time that is exponentially distributed. The steady state analysis of the inventory model is performed using the well-known matrix analytic methods. An optimization along with a couple of illustrative numerical examples are presented.
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Chakravarthy, Srinivas R., "An inventory system with Markovian demands, phase type distributions for perishability and replenishment" (2010). Industrial & Manufacturing Engineering Publications. 47.