Abstract
A model of a perishable product inventory system operating in a random environment is studied. For the sake of simplicity, the stochastic environment is considered to alternate randomly over time between two states 0 and 1 according to an alternating renewal process. When the environment is in state k , the items in the inventory have a perishing rate k µ , the demand rate is k λ and the replenishment cost is k CR . Assuming instantaneous replenishment at the epoch of the first demand after the stock-out and associating a Markov renewal process with the inventory system, the stationary distribution of the inventory level and the performance of various measures of the system evolution are obtained. Numerical examples illustrate the results obtained. OPSOMMING
Highlights
Various stochastic models of inventory systems have been studied recently by Yadavalli and Joubert [13], Yadavalli et al [12]
In the stochastic analysis of such inventory systems, it is generically assumed that the distributions of the random variables representing the number of demands over a period of time, the lifetime of the product and the lead-time remain the same and do not change throughout the domain of the analysis
We investigate a perishable product inventory system operating in a random environment
Summary
Various stochastic models of inventory systems have been studied recently by Yadavalli and Joubert [13], Yadavalli et al [12]. When the environment is in state k , the items in the inventory have a perishing rate μk , the demand rate is λk and the replenishment cost is CRk. Assuming instantaneous replenishment at the epoch of the first demand after the stock-out and associating a Markov renewal process with the inventory system, the stationary distribution of the inventory level and the performance of various measures of the system evolution are obtained. This paper is structured as follows: Paragraph 2 provides the assumptions and notation of a model of an inventory system operating in a random environment and certain auxiliary functions are obtained in Paragraph 3. Considering the point process of r -events occurring in an interval in which there is no change in the state of the environment, the function hr,k (t) are defined as follows: hr ,k.
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