Production control of a manufacturing system subject to deterioration

In this paper we consider a control problem for a manufacturing system comprising a single machine subject to a deterioration process. The system produces a single part type and the model is fluid. The objective is to minimize a long term average cost index which penalizes both inventory surplus and backlog. The machine deterioration rate depends on the production rate and a maintenance operation is performed when the deterioration reaches a specified alarm level. In this paper it is shown that the optimal control operates the machine alternating the maximum production capacity with idle or conservative periods (policy μ-d-μ) if the machine deterioration rate is a concave function of the production rate while it is a continuous feedback function of the buffer level if the deterioration rate is convex. This confirms the results obtained in the past for Markov failure prone systems.