An artificial neural network based mathematical model for a stochastic health care facility location problem

This research is conducted to investigate the problem of locating the trauma centers and helicopters' station in order to optimize the trauma care system. The stochastic characteristics of the system, such as stochastic transferring time of the patients, stochastic demand and stochastic servicing time of the patients in trauma centers are taken into account. The problem is first modeled as a stochastic mixed-integer linear mathematical model. In the proposed model, minimizing the total cost, minimizing the transferring time, and minimizing the waiting time inside the trauma center are considered as the three separate objectives. The third objective cannot be expressed by an analytical expression because of the complexity inside a trauma center. Therefore, an artificial neural network (ANN) is first trained by a simulation model and then is utilized to estimate the third objective function. A hybrid multi-objective algorithm is developed based on a non-dominated sorting water flow algorithm in order to search the solution space. Different numerical examples are applied to study the performance of the proposed method. The computational results show that the combination of simulation, ANN, and optimization technique provides an effective means for the highly complex optimization problems.