A DOUBLE BAND CONTROL POLICY OF A BROWNIAN PERISHABLE INVENTORY SYSTEM

The blood bank system is a typical example of a perishable inventory s ystem. The commodity arrival and customer demand processes are stochas tic. However, the stored items have a constant lifetime. In this study , we introduce a diffusion approximation to this system. The stock lev el is represented by the amount of items arriving during the age of th e oldest item; it is assumed to fluctuate as an alternating two-sided regulated Brownian motion between barriers 0 and 1. Hittings of level 0 are outdatings and hittings of level 1 are unsatisfied demands. Also , there are two predetermined switchover levels, a and b, with 0 less than or equal to a < b less than or equal to 1. Whenever the stock lev el process upcrosses level b, the controller generates a switch in the drift from gamma = gamma(0) to gamma = gamma(1), while downcrossings of level a generate switches from gamma(1) to gamma(0). A useful marti ngale is introduced for analyzing the stationary law of the controlled process as well as the total expected discounted cost.