# Coordination in Emergency Response System Design:
## 1 Introduction  
Ensuring public safety requires preparedness for a variety of emergencies. These include traffic accidents, medical emergencies, search and rescue operations, terrorist attacks, structure fires, and industrial accidents. Natural disasters, such as wildfires, flooding, earthquakes, hurricanes, and tornados also require appropriate emergency response planning. The initial response to such emergencies is almost always carried out by local authorities, including the police, emergency medical technicians (EMTs) and fire fighters. In case of larger-scale disasters or when specialized response teams are required, such as hazardous material (hazmat) releases, assistance from regional and federal authorities may become necessary. In the U.S., the Incident Command System constitutes a standardized approach to the command, control, and coordination of emergency response providing a common hierarchy within which responders from multiple agencies can be effective [1]. In Canada, the National Emergency Response System enables coordinated efforts in responding to emergencies [2]. For example, in Ontario, the provincial resources to respond to the chemical, biological, radiological, nuclear, or explosive incidents are clearly stated in [3]. Teamsfrom the Windsor, Toronto, and Ottawa fire departments are available to respond to these incidents at the technician level, whereas six smaller cities have committed to make teams available at the operations level for such emergencies. The efficient deployment and coordination of services, agencies and personnel to provide the earliest possible response to an emergency is crucial for reducing its undesirable effect on the people and the environment. One of the factors that determine the timing of the response is the location, where the various emergency response resources are stationed. The presence of all these teams at the site of an emergency is often required to ensure the effectiveness of the response. Despite the need for coordination, the operations research literature focuses on the location of a single response resource, e.g., ambulance stations or fire stations (see Section 2 for an overview). In this paper, we address this gap in the literature by studying the design of an emergency response network that comprises multiple specialty teams that need to attend the incident simultaneously. Of course, each team can undertake a few activities at the incident site before the others arrive, which could be included in an operational level plan. We adopt a strategic perspective in this paper and aim at maximizing the time the specialty teams can jointly respond to the emergency. One of the proxies that can be used for measuring the level of coordination among different response teams is the time between their arrival at the scene of emergency. Since the skills, expertise, and equipment of all the teams are needed for an effective response, lower wait times would indicate higher levels of coordination. Traditionally, a possible emergency site is considered \"covered\" by a response facility, if it is within a predetermined distance (or time) from the facility. The maximum covering location problem, first introduced by [4], can be considered as the basic building block of emergency response network design. The problem involves determining the locations of a given number of response facilities to maximize the number of people who would receive the services of the response team in a timely fashion. In this paper, we present a formulation for the maximal covering problem with two resources, where the concept of coverage is expanded to include an acceptable wait time as well as a desirable response time for each of the teams. Note that this conceptual framework would also apply for the problem with more than two resources, albeit the arising formulation would be more tedious due to the higher dimensionality of the response times and wait times discussed in Section 3. We apply the proposed methodology for studying the hazmat incident response network in Chengdu City, China.