Geoscience Reference
In-Depth Information
Chapter 9
Location Problems with Multiple Criteria
Stefan Nickel, Justo Puerto, and Antonio M. Rodríguez-Chía
Abstract This chapter analyzes multicriteria continuous, network, and discrete
location problems. In the continuous framework, we provide a complete description
of the set of weak Pareto, Pareto, and strict Pareto locations for a general Q-criteria
location problem based on the characterization of three criteria problems. In the
network case, the set of Pareto locations is characterized for general networks as
well as for tree networks using the concavity and convexity properties of the distance
function on the edges. In the discrete setting, the entire set of Pareto locations
is characterized using rational generating functions of integer points in polytopes.
Moreover, we describe algorithms to obtain the solutions sets (the different Pareto
locations) using the above characterizations. We also include a detailed complexity
analysis. A number of references has been cited throughout the chapter to avoid the
inclusion of unnecessary technical details and also to be useful for a deeper analysis.
Keywords Level
curves
￿
Networks
￿
Pareto
locations
￿
Pareto-optimal
￿
Rational functions ￿ Tree networks
9.1
Introduction
Very often, locational decisions involve the investment of a significant amount of
money. It will be therefore very probable that a locational decision is made by a
group of Q decision makers (DM). In turn, it is very likely that each DM will choose
a median function to evaluate the quality of a new location, but the weights assigned
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