The maintenance policies of computed tomography scanners in most hospitals are based on empirical knowledge and often following the manufacturer’s advice. In developing countries, the frequency of use of this equipment may be superior than recommended due to scarcity of resources, which could affect the optimal maintenance policy. Taking into account the budget and capacity of the equipment that public and private hospitals have in the administration, it is crucial to find an adequate decision support system that serves as a tool for the design of maintenance policies. The objective of this research is to develop an optimization model that allows making better decisions when preparing maintenance policies. The computed tomography scan is used in several diagnostic procedures, on different specialties, as it is a non-invasive exploration of the body. A continuous-time Markov chain model is proposed to model the different states of the equipment (working, requiring preventive maintenance, broken down). An optimization model is proposed with the objective of maximizing the benefit generated by the operating equipment and requiring maintenance. Budget constraints are considered. Two optimization methods are proposed and compared to solve the optimization model: an exhaustive search algorithm to understand the behaviour of the solution surface generated by the objective function and a meta-heuristic based on gradient-ascent to find near-optimal solutions in a reasonable time.