Convex backorders of a rationing inventory policy with two different demand classes

We study the constant critical level policy for fast‐moving items of an inventory system facing random demands from two customer classes (high and low priority). We consider a continuous review [Formula: see text] policy with continuously distributed demands. Using the properties of the nondecreasing stationary stochastic demand and the threshold clearing mechanism we formulate a convex cost minimization problem to determine the optimal parameters of the critical level policy, which can be optimally solved through KKT conditions. For instances we tested, computational results show that the critical level policy induce a benefit on average [Formula: see text] and [Formula: see text] against the round‐up and separate stock policies respectively.