A Limit Property for the Optimal Control of a Replacement Problem with Maintenance Under Uncertainty

An important property for the replacement decisions with maintenance under uncertainty is found and accordingly, a smart computation algorithm is created to find the optimal solution to the multistage optimal control problem(Dogramaci and Fraiman, 2004). This paper gives a proof for a limit property of this optimal control, i.e., the optimal control for the D-F problem is nondifferentiable at the points where the replacement opportunities are available. That is to say, the optimal control of the D-F problem is different from the K-S problem no matter how nimble an organization is.