Simultaneous Optimization of Preventive Maintenance and Replacement Policy for Machines : A Modern Control Theory Approach

In this paper, the problem of machine replacement in a changing technological environment is formulated as a problem in modern control theory. The objective is to maximize the present value of all future net profits over a class of infinite chains of machines where each link in the chain represents a uniform length replacement cycle with identical preventive maintenance. The control is effected by varying (i) the length of the replacement cycle, and (ii) the schedule of preventive maintenance. The optimal control is determined by applying the maximum principle of Pontryagin and resulting influence functions are provided economic interpretations. PDF version: Sethi, S.P. “Simultaneous Optimization of Preventive Maintenance and Replacement Policy for Machines: A Modern Control Theory Approach,” Management Sciences Research Report #223, GSIA, Carnegie-Mellon University, 1971