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Probabilistic analysis of a continuous review perishable inventory system with Markovian demand, Erlangian life and non-instantaneous lead time. (English) Zbl 0636.90017

Summary: This article obtains an explicit cost expression for a continuous review (S,s) ordering policy inventory system of perishable items, in the stationary case. The cost expression is closely related to the stationary distribution of the stochastic process L(t), representing the inventory at any time t. The stochastic behaviour of the process \(\{\) L(t), \(t\geq 0\}\) is characterized by identifying an imbedded MRP. The demands of the system are governed by a Poisson process. The items in the inventory have a useful life time characterized by an Erlangian distribution. The lead time is a random variable with specified probability distribution. It is assumed that the demands that arrive when the inventory is zero are lost.

MSC:

90B05 Inventory, storage, reservoirs
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
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References:

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