On the safety stock problem for random delivery processes

Inventory models are considered in which the delivery of an order occurs not on one occasion but at random moments of a period in random parts. We give two extensions of the reliability type inventory model of A. Prékopa. In this model a known constant demand rate is assumed and a simple approximate formula is given for the initial stock of the order period which serves as safety stock and ensures a continuous supply during the whole order period on a prescribed probability level. This formula is widely used in practice for safety stock planning in the case when deliveries in random parts occur.We formulate a generalized version of the random delivery process and derive the exact solution of the safety stock which can be applied also for the previous model. In the second model a random demand rate is considered together with a random delivery process. An exact solution method and a simple approximate formula for the safety stock will be discussed. We have experiences in the application of these models both in a steel works and a textile factory in Hungary.