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For the past few years, hospitals have been forced to improve their productivity, with surgical centers being one of the sectors with higher costs within such organizations, but also the ones that generate the most revenue. Thus, optimization methods for surgical programming are tools that can be used to reduce queues and idleness in these sectors and consequently achieve the aforementioned goals. The ”Problem of Programming Multiple Surgical Resources with Multiple Steps”consists in allocating the existing resources to each surgery stage that a patient will need to go through, considering the different needs, sequence and specificities of each of them, and then scheduling these steps in time. This type of problem is classified in the current literature as an NP-hard problem, being described as a Flexible Job Shop with blocking and an objective function that seeks to minimize the number of patients not served and the total makespan. The general purpose of this research is to propose a mathematical model and a constructive heuristic for this type problem. The proposed model explores the mathematical model Multi-Mode Blocking Job Shop (MMBJS) presented in Pham and Klikert (2008) suggesting improvements through the use of an alternative Mixed Integer Linear Programming that aims to: reduce the computational effort, adjust the makespan calculation and suggest a strategy of patients prioritization. In order to prove the benefits of the proposed enhancements, computational tests were performed to compare the MMJBS model and the proposed model, identifying that for instances where in which all patients are attended, the solutions found by CPLEX for both models are the same, but with a lower computational time the proposed model (45% average reduction). Also, other computational tests were performed to observe the behavior of the model with different configurations of resources. For instances with 15 patients, the tests indicate that the computational time to find the optimal solution is greater than 2 hours of processing. Thus a constructive heuristic is proposed, it aims to generate feasible solutions with little computational effort. The proposed heuristic allocates each surgery stage of a patient to the necessary resources, respecting the available windows and seeking to reduce the total slack in the system. An example of the application of the constructive heuristic is also presented. At last, future works proposals are presented in the final chapter of this dissertation.

Técnicas de pesquisa operacional aplicadas ao problema de programação de cirurgias eletivas.