The maintenance department in a hospital is responsible for ensuring the safety of medical equipment and their availability while keeping the operation costs minimal. The selection of the best maintenance strategy is a key decision to reduce the equipment downtime, increase the availability, and bring down the maintenance costs. In this paper, we use an integrated approach that includes several tools from the literature, namely, the Analytical Hierarchy Process (AHP), the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and the mathematical optimization (especially mixed integer problems MILP) to provide the decision maker of the maintenance department with an entire solution to the problem at hand. These three tools are introduced to 1) determine the criticality of medical equipment based on a multi-criteria analysis, 2) rank the different maintenance strategies based on their (benefits) importance to the hospital and 3) select the optimal maintenance strategy for each device while keeping the total maintenance costs within a predetermined budget. We applied our approach to a case study at the Hospital of “Habib Bourguiba” in Tunisia, and the numerical results show the efficiency of our approach to improve the availability and the reliability of high risk medical devices.