• PROBABILISTIC ANALYSIS OF INVENTORY SYSTEMS WITH SALES TIME DEPENDING ON INVENTORY THRESHOLD

Abstract

A production and sales system is considered. In model 1 stock arrives in accordance with Poisson process and the arrival starts sale immediately. In addition a machine produces one product at a time and the production time is general. The sale time for the production of the products start with a probability p on all production epochs and if the sale time does not begin the products are stored in the inventory till a threshold level is reached and after that the sale time starts. In model 2 there is no stock arrival process but a machine with exponential life time produces the products and the repair time of the machine is also exponential. Assuming that the products are sent for sales as in model 1, joint Laplace transforms of time to sales and sales time, their means and a numerical result are presented for the two models.