Pathwise properties and performance bounds for a perishable inventory system

We study a perishable inventory system under a fixed-critical number order policy. By using an appropriate transformation of the state vector, we derive several key sample-path relations. We obtain bounds on the limiting distribution of the number of outdates in a period, and we derive families of upper and lower bounds for the long-run number of outdates per unit time. Analysis of the bounds on the expected number of outdates shows that at least one of the new lower bounds is always greater than or equal to previously published lower bounds, whereas the new upper bounds are sometimes lower than and sometimes higher than the existing upper bounds. In addition, using an expected cost criterion, we compare optimal policies and different choices of critical-number policies.