A single product perishing inventory model with demand interaction

Abstract

The paper describes a single perishing product inventory model in which items deteriorate in two phases and then perish. An independent demand takes place at constant rates for items in both phases. A demand for an item in Phase I not satisfied may be satisfied by an item in Phase II, based on a probability measure. Demand for items in Phase II during stock-out is lost. The re-ordering policy is an adjustable (S, s) policy with the lead-time following an arbitrary distribution. Identifying the underlying stochastic process as a renewal process, the probability distribution of the inventory level at any arbitrary point in time is obtained. The expressions for the mean stationary rates of lost demand, substituted demand, perished units and scrapped units are also derived. A numerical example is considered to highlight the results obtained.