A double band control policy of a brownian perishable inventory system

The blood bank system is a typical example of a perishable inventory system. The commodity arrival and customer demand processes are stochastic. However, the stored items have a constant lifetime. In this study, we introduce a diffusion approximation to this system. The stock level is represented by the amount of items arriving during the age of the oldest item; it is assumed to fluctuate as an alternating two-sided regulated Brownian motion between barriers 0 and 1. Hillings of level 0 are outdatings and hillings of level 1 are unsatisfied demands. Also, there are two predetermined switchover levels, a and b, with 0 ≤ a < b ≤ 1. Whenever the stock level process upcrosses level b, the controller generates a switch in the drift from γ = γ₀ to γ = γ₁ while downcrossings of level a generate switches from γ₁ to γ₀. A useful martingale is introduced for analyzing the stalionary law of the controlled process as well as the total expected discounted cost.