Data-driven approach for demand estimation and optimization of EMS system operation

Abstract

As a consequence of the computerization of emergency medical service (EMS) system, enormous demand records were generated that lead to a shift from a priori reasoning or expert-based demand estimation to the data-centered demand estimation. As we deepened our understanding of an EMS system, the optimization models for the EMS system were extended and improved. However, the demand of an EMS system have many challenging properties for data analysis such as spatio-temporal variability and batch arrivals. This dissertation started with the suggestion of a novel demand model which appropriately captures the characteristics of EMS demand. Then, we develop a probabilistic ambulance location model which exploits the proposed demand model. Finally, we present a distributionally robust ambulance location model that capable to handle the uncertainty and ambiguity in a demand model. In chapter 2, we propose a spatio-temporal demand model that incorporates batch arrivals of EMS calls. Specifically, we construct a spatio-temporal compound Poisson process which consists of a call arrival model and call size model. We build our call arrival model by combining two models available in the existing EMS demand modeling literature – artificial neural network and spatio-temporal Gaussian mixture model. For the call size model, we develop a $k$-inflated mixture regression model. This model reflects the characteristics of EMS call arrivals that most calls involve one patient while some calls involve multiple patients. We also screened effective spatio-temporal variables and mixture distribution for the call size model. We demonstrate the proposed demand model’s potential benefit by suggesting two applications in the context of EMS system design. In chapter 3, we present a probabilistic ambulance location model which exploits batch arrivals queuing property to demonstrate the benefit of the proposed demand model. In doing so, we generalize hypercube queuing approximation model to handle batch arrivals. The validity of the generalized model is examined by comparing the busy fraction of ambulances with the values from EMS simulation. To apply the proposed location problem to demand distribution estimated in chapter 2, we adopt demand aggregation technique to generate demand node. The potential benefit of the proposed demand model is evaluated through various experiments. Our experimental results show that the loss probability is underestimated if batch arrivals are ignored. We also observed that the degree of the underestimation becomes more severe when the deviation from the single arrival assumption is larger as measured by the index of dispersion of arrival data. In chapter 4, we propose a distributionally almost robust ambulance location model and discuss the procedure of ambiguity set construction for Poisson demand. We provide a discussion on the risk level of ambiguity set, within which the true distribution asymptotically falls into the designed ambiguity set. Using a simple facility location model we first demonstrate the solution performance of distributionally robust optimization compares to almost robust optimization. The result shows that the solutions from robust optimization and distributionally robust optimization with low risk level can easily lose its feasibility when the demand distribution has a certain ambiguity. The distributionally robust optimization provides a solution that is more costly than the solution of robust optimization for its additional robustness toward ambiguity. The probabilistic model in chapter 3 is extended to distributionally robust version and applied to Daejeon demand. Based on the result we provide some suggestions for EMS operators.