The effect of finite buffers on the optimal safety stock for unreliable systems

In this paper we consider a single part-type, single unreliable machine production system under a fluid approximation to describe the part flow through the system. We will assume that only a finite space is available for waiting demand and customers arriving when the backlog buffer is full are rejected, incurring in a penalty. The problem is to determine a production control which minimizes an infinite horizon average loss/backlog/surplus cost. In the infinite buffer capacity case, this problem is solved by a hedging point policy. In this paper we consider the finite capacity case, and based on an equation presented in a previous paper we discuss the effect of some meaningful parameters on the computed hedging point and the effect of finite buffers on the optimality of Just In Time (JIT) policies. An adaptive control algorithm is realized to determine the optimal hedging point when the system parameters are not known and must be estimated through the observation of the system.