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An emergency is a situation that causes an immediate risk to the property, health, or lives of civilians and can assume a variety of forms such as traffic accidents, fires, personal medical emergencies, terrorist attacks, robberies, natural disasters, etc. Emergency response services (ERSs) such as police, fire, and medical services play crucial roles in all communities and can minimize the adverse effects of emergency incidents by decreasing the response time. Response time is not only related to the dispatching system, but also has a very close relationship to the coverage of the whole network by emergency vehicles.

The goal of this dissertation is to develop a model for an Emergency Management System. This model will dynamically relocate the emergency vehicles to provide better coverage for the whole system. Also, when an emergency happens in the system the model will consider dispatching and relocation problem simultaneously. In addition, it will provide real-time route guidance for emergency vehicles. In summary, this model will consider three problems simultaneously: area coverage, vehicle deployment, and vehicle routing.

This model is event-based and will be solved whenever there is an event in the system. These events can be: occurrence of an emergency, change in the status of vehicles, change in the traffic data, and change in the likelihood of an emergency happening in the demand nodes.

Three categories of emergency vehicle types are considered in the system: police cars, ambulances, and fire vehicles. The police department is assumed to have a homogeneous fleet, but ambulances and fire vehicles are heterogeneous. Advanced Life Support (ALS) and Basic Life Support (BLS) ambulances are considered, along with Fire Engines, Fire Trucks, and Fire Quints in the fire vehicle category.

This research attempts to provide double coverage for demand nodes by non-homogenous fleet while increasing the equity of coverage of different demand nodes. Also, the model is capable of considering the partial coverage in the heterogeneous vehicle categories. Two kinds of demand nodes are considered, ordinary nodes and critical nodes. Node demands may vary over time, so the model is capable of relocating the emergency fleet to cover the points with highest demand. In addition, an attempt is made to maintain work load balance between different vehicles in the system. Real-world issues, such as the fact that vehicles prefer to stay at their home stations instead of being relocated to other stations and should be back at their home depots at the end of the work shift, are taken into account.

This is a unique and complex model; so far, no study in the literature has addressed these problems sufficiently. A mathematical formulation is developed for the proposed model, and numerical examples are designed to demonstrate its capabilities. Xpress 7.1 is used to run this model on the numerical examples. Commercial software like Xpress can be used to solve the proposed model on small-size problems, but for large-size and real-world problems, an appropriate heuristic is needed. A heuristic method that can find good solutions in reasonable time for this problem is developed and tested on several cases. Also, the model is applied to a real-world case study to test its performance. To investigate the model's behavior on a real-world problem, a very sophisticated simulation model that can see most of the details in the system has been developed and the real case study data has been used to calibrate the model. The results show that the proposed model is performing very well and efficient and it can greatly improve the performance of emergency management centers.