Geoscience Reference
In-Depth Information
Chapter 18
Demand Point Aggregation for Some Basic
Location Models
Richard L. Francis and Timothy J. Lowe
Abstract
Location problems occurring in urban or regional settings may involve
many tens of thousands of “demand points,” usually individual residences. In
modeling such problems it is common to aggregate demand points to obtain
tractable models. We discuss aggregation approaches to a large class of location
models, consider various aggregation error measures, and identify some effective
measures. In particular, we focus on an upper bounding methodology for the error
associated with aggregation. The chapter includes an example application.
Keywords
Aggregation Demand points Location
18.1
Introduction
Many location problems involve locating services (called
servers
) with respect to
customers of some sort (called
demand points
, and abbreviated as DPs). Usually
there is travel between servers and DPs, so that travel distances, or (more generally)
travel costs, are of interest. Location models represent these travel costs, and
solutions to the models can provide locations of the servers of (nearly) minimal cost.
For topics on location models and modeling, see Daskin (
2013
), Drezner (
1995
),
Drezner and Hamacher (
2002
), Francis et al. (
1992
), Handler and Mirchandani
(
1979
), Love et al. (
1988
), Mirchandani and Francis (
1990
), and Nickel and Puerto
(
2005
).
A common difficulty with modeling location problems that occur in urban or
regional areas is that the number of DPs may be quite large, since each private
residence might be a DP. In this case it may be impossible, and also unnecessary, to
include every DP in the corresponding model. Further, the models may be NP-hard
to optimize (Kariv and Hakimi
1979
). For problems as diverse as those including
