Research On Locating Of Emergency Medical Service System Based On Distributionally Robust Optimization Method

Emergency medical service(EMS)system is an important part of the modern healthcare system.An efficient EMS system can respond quickly to emergency requests,transport critical patients,provide timely treatment,and save lives to the fullest extent possible.This paper focuses on the uncertainty of emergency medical demand and uses distributionally robust optimization(DRO)to study the location problem of EMS systems.The paper specifically covers the following four areas:1.A DRO model based on φ-divergence for optimizing the location of an EMS system.The objective is to minimize the total investment cost subject to the constraint that the maximum expected number of ambulances dispatched by each station to all emergency locations is less than or equal to the number of ambulances owned by the station.An ambiguity set is constructed using φ-divergence to model the uncertain demand distribution of emergency requests.φ-divergence is used to measure the similarity between the true probability distribution and the empirical distribution of emergency medical demands.Based on the constructed ambiguity set,a DRO expectation constraint is established to characterize the service level of the EMS system.The service level constraint is then reformulated into a quadratic programming constraint using duality theory,and a commercial solver is used for optimization.Finally,numerical examples are used to verify the effectiveness of the model and conduct sensitivity analysis on the model parameters.2.A two-stage DRO model based on Wasserstein-metric for optimizing the location of an EMS system.The objective is to minimize the total cost of constructing,purchasing,and operating the EMS system.The first stage optimizes the location of the stations by minimizing the expected total cost,and the second stage optimizes the allocation of ambulances to each station and the dispatching of ambulances to emergency demand sites by minimizing the operating cost.An ambiguity set is constructed using Wasserstein-metric to model the uncertain demands distribution of emergency medical services.Wasserstein-metric is used to quantify the distance between the true probability distribution and the empirical distribution of emergency medical demands and construct an ambiguity set that contains all potential true probability distributions.Based on the constructed ambiguity set,a DRO chance constraint is established to characterize the service level of the EMS system.Duality theory,value-at-risk(VaR)outerapproximation,and conditional value-at-risk(CVaR)inner approximation methods are used to reformulate and solve the DRO model.Finally,numerical examples are used to compare the three reformulated models and conduct sensitivity analysis on the model parameters.3.Physically bounded DRO model for optimizing the location of EMS system.Physical bounds information is introduced to limit the uncertainty range of the DRO chance constraint to a reasonable range,making the optimization model more realistic.Duality theory,CVaR inner approximation,and bilinear programming methods are used to reformulate and solve the DRO model.A comparative study of the three DRO models in terms of computational efficiency,accuracy,and applicability.The study aims to provide guidance for selecting the appropriate DRO model for optimizing the location of EMS systems under different scenarios.4.A multi-period distributionally robust optimization for location of EMS System.To address the uncertain emergency medical demands in dynamic environments,a multi-period planning model for emergency medical service systems based on Wasserstein-metric is established.The model is reformulated into a mixed-integer programming model using dual theory,and solved using both generalized Benders decomposition method and commercial solvers.Finally,the effectiveness of the model is verified through numerical examples.