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.