Optimal preventive maintenance,protection, and replacement of a revenue-earning asset

The problem of determining the optimal pattern of expenditure on preventive maintenance or protection for a revenue-earning asset subject to catastrophic breakdown or destruction is discussed. It is assumed that the probability of breakdown at any time depends on the age of the asset and on the current rate of prevention expenditure. The objective considered is the maximization of the expected present value of revenues earned net of prevention and replacement costs. Three distinct cases are discussed: (a) when revenue is earned only until breakdown; (b) when there is automatic replacement following a breakdown; and (c) when there is the option of periodic replacement. Use of the Pontryagin maximum principle enables the determination of the optimal prevention schedules in all cases. In addition, when periodic replacement is possible the optimal replacement interval can be determined. Numerical methods are required to obtain solutions.