Technical Note—Average Cost Optimality in Partially Observable Lost-Sales Inventory Systems

We consider a partially observable lost-sales inventory system, in which the inventory level is observed only when it reaches zero. We use the vanishing discount factor approach to prove the existence of a stationary optimal policy for the average cost minimization. As our main methodological contribution, we provide a way to verify the key condition of the vanishing discount factor approach—the uniform boundedness of the relative discounted value function. To accomplish that, we construct a valid policy, which, in a certain sense, “copies” the actions of another policy for the process with a different initial state. To the best of our knowledge, this paper is the first one on partially observable inventory models under the average cost criterion.