Systems of Cities and Facility Location

P. Hansen, J. Henderson, M. Labbe, J. Peeters, J. Thisse

• Publisher: Taylor & Francis
• Year: 2013
• Print ISBN: 9780415274753
• eBook ISBN: 9781136473661
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

First Published in 2001. This book contains two essays: the first examines optimal facility location, according to a variety of economic criteria; the second develops a theory of international trade in which a region is regarded as a system of cities.

Facility Location Analysis

PIERRE HANSEN,* MARTINE LABBÉ,† DOMINIQUE PEETERS‡ and JACQUES-FRANÇOIS THISSE§

RUTCOR, Rutgers University,* GRESG, Université de Strasbourg l,† Department of Geography‡ and CORE,§ Université Catholique de Louvain

Acknowledgements

The authors are indebted to R. Arnott, H. Beguin, P. Hanjoul, G. Wesolowsky and L. Wolsey for their comments on previous drafts of this article.

INTRODUCTION

Facility location analysis deals with the problem of locating new facilities with regard to existing facilities and clients in order to optimize one or several economic criteria. Examples of facilities are plants, warehouses, schools, hospitals, administrative buildings, department stores, military bases, waste material dumps, ambulance or fire engine depots, etc. Alfred Weber is generally given credit for having introduced the first location model in a book published in 1909. Perhaps more importantly, he set up a paradigm for location based on the minimisation of transportation costs which was to have a lasting influence on the subsequent developments. However, it was only after 1960 that significant progress occurred and that location theory emerged as a discipline. Some general remarks on the state of the art justify the contents and presentation of this article.

Most facility location models proposed so far are built within the framework of Operations Research. As such, they are basically normative models. Their economic setting may appear naive to an economist because of the simplifying assumptions required to make them computationally tractable. On the other hand, they display enough versatility to accommodate a large number of different situations. This point will be stressed in what ensues. Another consequence of their origin is the emphasis generally laid in the quoted papers on algorithmic procedures. This aspect has become one of the most vivid parts of facility location analysis and has provided useful insights into Mathematical Programming. We have tried to tell the reader the gist of the solution methods without going into too many computational details.

A recent bibliography devoted to facility location analysis contains over 1500 references; see Domschke and Drexl [38]. A glance at the papers reveals a large variance of problems. Therefore we had to perform a selection and a classification at the same time. First, we decided to present only what we considered to be basic models. More specifically, we have discarded dynamic, stochastic and multicriteria location models. It by no means prejudges their lack of interest, but it is our contention that the static, deterministic and single-criterion models are rich enough to illustrate the underlying principles of location theory. Second, a detailed classification of location models may be problematic because of the absence of a unifying framework. However, it is now classical to divide them up into three chapters, hence our choice to organize the article in three parts.

We take it in Chapter 1 that the set of possible locations for the facilities is a subset of the plane that has a two-dimensional extension (i.e. whose interior is nonempty). The corresponding models are called continuous location models. The unknowns are the coordinates of the facilities to be settled. The solution methods generally resort to Nonlinear Programming. Their field of application in the real world is perhaps meagre, but they provide us with fruitful insights on mechanisms that prevail during the location decision process.

In Chapter 2, we assume that the set of possible locations is finite. The models are then called discrete location models. Their solution methods generally belong to Combinatorial and Integer Programming. They have been paid far and away the most attention by the practitioners. A drawback is that the list of possible sites must be carefully drawn up, omissions being sometimes disastrous and yet unnoticed. An advantage is their flexibility, which allows the practitioner to incorporate irregularities in the landscape and characteristics of the facility and of the client without changing the formal structure, hence the algorithms, while the same operation often dramatically complicates continuous models.

Finally, in Chapter 3, the set of possible locations is given by a network constituted by a finite number of (topological) arcs. Facilities can be located at the extremities or at the intermediate points of the arcs. The corresponding models are called network location models. They are motivated by the fact that, in many real-world cases, facilities can be established anywhere along a transportation or communication network. Their most distinctive feature is that it is frequently possible to identify a finite subset of the network which always contains an optimal solution. This allows one, therefore, to determine an optimal ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Original Copyright Page
• Contents
• Introduction to the Series
• Preface
• FACILITY LOCATION ANALYSIS
• SYSTEMS OF CITIES AND INTER-CITY TRADE