Stochastic Point Processes in a Storage Model

Abstract

A warehouse with a storage capacity of n units is considered. While the units of input arrive according to a general stationary point process ? (t), the stored items are cleared with the arrival of a bulk order which is assumed to arrive according to another general stationary point process ? (t). When the inputs exceed n, there is a cost associated with an emergency clearance. Further there are costs associated with shortage when the bulk order arrives to find the store empty and costs of maintenance of the n unit warehouse. The techniques of stationary point processes are employed to study this selective interaction and to arrive at the total cost function at any time t. This total cost function is used to obtain the optimal warehouse capacity.