{'fraction_non_alphanumeric': 0.018137847642079808, 'fraction_numerical': 0.0012091898428053204, 'mean_word_length': 5.331632653061225, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Modeling and Optimization for Emergency Medical Services Network

Ambulance offload delays have become a challenging concern for emergency healthcare service providers. These delays often occur when the number of patients in the emergency department (ED) exceed the designed capacity such that ED cannot accept an incoming patient immediately, thereby forcing the ambulance and crew to wait with the patient until a bed becomes available. In this paper, we analyze and optimize the emergency medical services network, including ambulance stations and EDs. The objective is to reduce ambulance offload delays and lessen the congestion of EDs. To this end, we first build a continuous-time Markov chain to characterize this network analytically. Next, from the perspectives of both ambulance stations and EDs, we develop resource configuration and optimization models for this network. We investigate the reasons for ED overcapacity and ambulance offload delays. Finally, we design an effective approach to reconfigure the resources in the emergency medical services network, leading to a new and better equilibrium. Note to Practitioners—This article is motivated by our collaborations with the Emergency Medical Service Center (also called 120 Center) and several hospitals in Shanghai, China. The Emergency Medical Service Center and ED of hospitals are the frontlines of healthcare services in Shanghai. They provide medical treatment services for acutely ill and injured patients, so the operation of this system is critical to the health of such patients. Today, the ambulance offloading delay poses a challenge to the Emergency Medical Service Center, as it reduces the usage of ambulances and crews, as well as putting patients at risk. Meanwhile, the EDs sometimes suffer from bed shortages and overcrowding. Emergency Medical Service Centers and hospitals are both striving to improve the performance of this system. We analyze the network, including both the ambulance station (AS) and ED, and formulate a continuous-time Markov chain model to describe the network states. Then, we propose two optimization models from both AS and ED perspectives with a series of approximation methods to overcome computational difficulties. We obtain the equilibrium through joint optimization of AS and ED and demonstrate some valuable insights for managing ambulances and beds in the ED. Methods presented in this article may help decision-makers in emergency medical services systems.