Discrete Models for Intermediate Storages under Stochastic Operational Conditions

Abstract

In this paper we investigate the operation of an intermediate storage assuming discrete stochastic operational conditions. The storage operates as a buffer. The material is collected into it and is withdrawn from the buffer for production. Deterministic constant withdrawal rate is supposed and the filling process is described by discrete random variables. The main question addressed here is the probability of material shortage as a function of the initial amount of material. For this purpose, an auxiliary function is defined and a difference equation is set for it. In a special case we present the solution of the difference equation, we compare the exact and simulated results, and we propose a method for the determination of unknown constants. We apply the results for expressing the initial amount of material necessary to a given reliability level. Finally, we compare the results of the discrete model with those of the continuous one.