Maintenance optimal control three-machine replacement model under technological breakthrough expectations

This paper addresses a finite-horizon profit maximization three-machine replacement problem. More precisely, a model is formulated allowing for preventive maintenance to slow down machine quality and profit reduction caused by obsolescence, to determine the timing of replacing an existing machine by another available machine with improved technology. This decision is considered under uncertainty regarding the introduction time of a machine with a not-yetachieved technology. Given an exponential probability distribution function of the introduction time, the optimality of a bang-bang nonincreasing preventive maintenance control is shown. Moreover, subproblems maximizing the expected discounted profit are analyzed. Closed-form solutions are provided to compare machines of different technologies and to derive an analytical sensitivity analysis concerned with many issues related to the problem. The results are not necessarily intuitive and simple. For example, different relationships between the planning horizon and the preventive maintenance switching time are presented for the three-machine problem versus the single-machine problem. The focus of this paper is on the formulation and the analytical analysis of the problem rather than on its computational aspects.