A novel probabilistic formulation for locating and sizing emergency medical service stations

The paper proposes a novel probabilistic model with chance constraints for locating and sizing emergency medical service stations. In this model, the chance constraints are approximated as second-order cone constraints to overcome computational difficulties for practical applications. The proposed approximations associated with different estimation accuracy of the stochastic nature are meaningful on a practical uncertainty environment. Then, the model is transformed into a conic quadratic mixed-integer program by employing a conic transformation. The resulting model can be efficiently addressed by a commercial optimization package. A special case is also considered and a class of valid inequalities is introduced to improve computational efficiency. Lastly, computational experiences on real data and randomly generated data are reported to illustrate the validity of the program.