Approaches for optimal location of emergency response vehicles

Abstract

Police, fire and emergency medical systems are all concerned with improving public safety, and share the common objective of responding to citizen calls for assistance as quickly as possible to reduce loss of life and injury. Optimization of emergency response vehicles location is a research area which is concerned with the location of one or more vehicles so as to satisfy objective function requirements such as providing fast and reliable service to customers. The most important decision facing any emergency response service is how many emergency vehicles to have, and on which site to locate them. A vast literature has developed out of the significant research interest in meeting this challenge. The literature review is separated into three sections depending on the objective function of the location models: Covering models, P-median models, and Center models. In the next chapter 3, we describe characteristics and performance criteria of emergency response services. The assumption is that if calls are answered and serviced quickly, then this will lead to customer satisfaction and compliance to regulatory standards for response time performance. The decision-maker is confronted with the elements of time and distance simultaneously. The time taken to get to an incident is necessarily dependent upon the distance to be travelled and the conditions experienced during the journey. Timeliness, cost minimization, coverage equity maximization and labor equity maximization are the most important objectives of emergency service systems. In this thesis we also, focused on the description of some methods to estimate travel distance and travel time. A crucial issue in locating emergency response vehicles is data availability. Collection and analysis of the available data point out one of the main problems of the system. Mathematical models may be very useful in dealing with emergency response vehicle location. In chapter 4, location models are classified according to their objectives, constraints, solutions, and other attributes. There has been an important evolution in the development of emergency vehicles location and relocation models over the past years. In this thesis, we attempted to provide an overview of emergency vehicles location models dedicated to capturing the complex time and uncertainty characteristics of most real-world problems. Chapter 5 concerns an elaborate description of the basic emergency response vehicles location models, mostly, in discrete space or networks, that are related to the public sector, such as ambulances, fire vehicles, police units. Static and deterministic location models assume that the nearest unit to a call for service is always available. Dynamic models can be used to periodically update emergency vehicles positions throughout the day. Probabilistic models deal with the stochastic nature of real-world systems. In these systems, models capture the stochastic aspects of facility location through explicit consideration of the probability distributions associated with modeled random quantities. Parameters, such as travel times, the location of clients, demand and the availability of servers are treated as random variables. The objective is to determine robust server/facility locations that optimize a given utility function, for a range of values of the parameters under consideration. Finally, in chapter 6 we present two applications of P- Median and Hypercube models. The solution of Hypercube model is the state probabilities and associated system performance measures such as workloads. As far as it concerns the P-Median model, the aim is to locate a fixed number of vehicles so as to minimize the weighted travel time of the system. In the end, we solve P-Median model for fixed number of servers and we implement the hypercube model using the assignment resulted from P-Median problem.