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This work aims to apply the Facility Location Problem in the Emergency Medical Service (EMS) of Belo Horizonte, Brazil. The objective is to improve two previous optimization models from literature to handle base locations and ambulances allocation/relocation problems. The proposed multi-period models introduce the concept of relocation to the local EMS, which allows ambulances to move among bases in different periods to raise the system coverage. This paper also proposes a bi-objective approach aiming to minimize the number of bases and maximize the coverage of demands, which is solved using the epsilon-constraint method. Results show that coverage levels increase by up to 31% for the deterministic approach and up to 24% for the probabilistic approach. Ambulances' relocation optimization might improve coverage levels by up to 21% for the deterministic approach and up to 15% for the probabilistic approach when change scenarios from static to multi-period. Also, since the multi-period model solutions result in installing a larger number of bases, the bi-objective approach is a powerful tool for the decision-maker. Bi-objective results suggest modest increments in the objective function when the stations' number exceeds 28 for the deterministic approach. The probabilistic approach increments in the objective function start to narrow above 30 installed stations.