A Continuous Review(S-1, S) Inventory Policy in which Depletion is due to Demand and Loss of Units

A stochastic model for an inventory system in which depletion of stock takes place due to random demand as well as random loss of items is studied under the assumption that the intervals between successive unit demands, as well as those between successive unit losses, are independently and identically distributed random variables having negative exponential distribution with respective parameters. We have derived the steady state probability distribution of the net inventory level assuming negative exponential delivery time under the continuous review (S-1, S) inventory policy. Also we have derived the total expected cost expression and necessary conditions to be satisfied for an optimal solution.