Sizing Intermediate Storages in Discrete Models under Stochastic Operational Conditions

Abstract

In this paper the appropriate size of an intermediate storage is investigated. The input process is described by a stochastic process and the output process is deterministic. Both filling time points and filled amounts of material are described by discrete random variables. We focus on the necessary volume of the intermediate storage for the material in order to avoid the overfilling. To solve the sizing problem for a given reliability, an auxiliary function is defined and a difference equation is set up for it. In special cases it is solved analytically. Overflow probabilities and expected time of overflow are compared in continuous and discrete models. Analytic results are compared to the results arising from Monte-Carlo simulations as well. In general cases approximate solutions are presented and used for determining the necessary volume of storage for the change of material.