Optimal control of a production-maintenance system with deteriorating items

A production process whose performance deteriorates over time is studied in this paper. It is assumed that the process performance can be measured in terms of the proportion of good units of end items produced. Using the pontryagin principle, the optimal scheduled production rate and preventive maintenance rate will be derived as a function of both production rate and proportion of good units. The controlled system can be modeled by a system of non-linear differential equations and its solution will be discussed numerically. The sensitivity analysis for varying system parameters will be discussed for different cases of demand rate.