Hedging point policies remain optimal under limited backlog and inventory space

In this note, we consider a fluid flow, single part-type, single unreliable machine production system with a bounded backlog/inventory space. We prove that, as in the unbounded case, the problem of minimizing an infinite horizon average demand loss/backlog/surplus cost is solved by a hedging point policy. An implicit equation is given, whose structure easily allows to numerically evaluate the optimal safety stock. The effect of system parameters on the optimal safety stock is analyzed and some numerical examples illustrate the presented results.