ROLLING HORIZON PROCEDURES FOR THE SOLUTION OF AN OPTIMAL REPLACEMENT PROBLEM OF n-MACHINES WITH RANDOM HORIZON

Abstract

In this paper a system consisting of independently operating n-machines is considered, where each machine follows a stochastic process of deterioration, which is associated with a cost function. It is assumed that the system is observed at discrete time and the objective function is the total expected cost. Also, it is considered that the horizon of the problem is random with an infinite support. In this case, the optimal replacement problem with a random horizon is modelled as a non-homogeneous optimal control problem with an infinite horizon and solved by means of the rolling horizon procedure. Then, a replacement policy is provided, which approximate the optimal solution. Finally, a numerical example through a program in Maple is presented.