3 Discrete Network Location Models

Undoubtedly, humans have been analyzing the effectiveness of locational decisions since they inhabited their first cave. We use the term “facility” here in its broadest sense. That is, it is meant to include entities such as air and maritime ports, factories, warehouses, retail outlets, schools, hospitals, day-care centers, bus stops, subway stations, electronic switching centers, computer concentrators and terminals, rain gages, emergency warning sirens, and satellites, to name but a few that have been analyzed in the research literature. The ubiquity of locational decision-making has led to a strong interest in location analysis and modeling within the operations research and management science community. The long and voluminous history of location research results from several factors. First, location decisions are frequently made at all levels of human organization from individuals and households to firms, government agencies and even international agencies. Second, such decisions are often strategic in nature. That is, they involve large sums of capital resources and their economic effects are long term. In the private sector they have a major influence on the ability of a firm to compete in the market place. In the public sector they influence the efficiency by which jurisdictions provide public services and the ability of these jurisdictions to attract households and other economic activity. Third, they frequently impose economic externalities. Such externalities include pollution, congestion, and economic development, among others. Fourth, location models are often extremely difficult to solve, at least optimally. Even the most basic models are computationally intractable for large problem instances. In fact, the computational complexity of location models is a major reason that the widespread interest in formulating and implementing such models did not occur until the advent of high-speed digital computers. Finally, location models are application specific. That is, their structural form (the objectives, constraints and variables) is determined by the particular location problem under study. Consequently, there does not exist a general location model that is appropriate for all potential or existing applications.