Frank
Plastria (Vrije Universiteit Brussel, Belgium)
Short
Biography
Frank
PLASTRIA was born in St Agatha Berchem (
Since
then he has been teaching several courses in Mathematical Programming,
Operations Research and Computer Science topics, and currently holds a post of
full professor at the same
university. He has been a research fellow at several universities abroad, such
as
His main scientific domains of interest are Mathematical Programming, Operations Research, in particular Location Theory and Data mining, Convex Analysis, Global Optimisation, Computational Geometry. He is the author of over 70 scientific papers in these fields, published in scientific books/ journals and congress proceedings, and of numerous press-columns concerning IT. He took part in the organisation of many international scientific conferences in operations research, and actively participates as speaker in several per year.
He is currently coordinator of the EURO Working Group on Locational Analysis (since 1994), see http://www.vub.ac.be/EWGLA/homepage.htm, and editor-in-chief of the journals `4OR, A Quarterly Journal of Operations Research Societies' (since 2001) (http://www.springeronline.com/journal/10288), and `Studies in Locational Analysis' (since 1997) (http://www.vub.ac.be/EWGLA/STUDIES/main.html). He has been president of the Belgian Operations Research Society Sogesci-BVWB, aka ORBEL (http://www.orbel.be/).
A more comprehensive Curriculum Vitae is available on line at his homepage http://homepages.vub.ac.be/~faplastr/, including a full list of publications.
Lecture to be presented in EWI 2007
Title
Distances
and covering in continuous space
Abstract
1
Distance
Distance is one of the central notions both in Location and in Logistics models.
Usually one considers that distance necessarily satisfies the basic properties
of a metric, but these are not always valid, in particular when distance is
considered in generalized settings, like economic or subjective distance.
In this talk we will first take a closer and critical look at the notion of
distance, and see what can still be done when weakening the metric properties.
Some very basic results still remain, like majority-like theorems for minsum
location problems, but not much more.
Then we will focus on continuous spaces (including networks) and see that a
basic requirement for being able to deploy the powerful mathematical machinery
of convex analysis automatically calls for the particular types of distances
which are derived from gauges. We will delve somewhat into the meaning,
interpretation and applications of several classes of such generalized
distances, and how new distance arise from the classical cases by simple
transformations. Particular attention will go to the planar case, which is not
only easiest without being trivial, but also the one of main interest in
standard applications. We will also take a brief look at the problems arising
when space is not considered to be homogeneous and barriers and/or local
modifications arise. Although several recent approaches are quite promising,
open problems and opportunities for research still abound in this area.
2 Covering
The other leading theme throughout the talk will be covering. This term collects
many variants of questions related either to threshold distances, ubiquitous in
emergency services and obnoxious facilities, or to minimum or maximum distances.
There are also some connections with competitive location problems and
transportation problems.
On the one hand we obtain full, empty and minimal or maximal partial covering
problems, on the other center or anti-center-like problems. We will review how
these types of problems can be solved using the classical Voronoilike diagram
constructs of computational geometry. Also convex geometry leads to important
results, allowing reduction of the continuous problems to discrete ones.
Many of these problems are considered to be easy, at least in their single
facility version and using the simplest distance measures. But we will see that
things become much harder when either more facilities are to be sited and/or
when more exotic distance notions are needed, as frequently happens in practice.
There is ample room here for novel work, both in exact approaches, but probably
even more in (meta)heuristic approaches.
References
[1] P.Bose, G.Toussaint, Computing the constrained euclidean, geodesic and link
centre of a simple polygon with applications, Studies in Locational Analysis, 15
(2000), 37-66.
[2] M.Cera, J.A.Mesa, F.A.Ortega, F.Plastria, Locating a central hunter on the
plane, Journal of Optimization Theory and Applications, to appear, 2007.
[3] F.Hurtado, V.Sacristán, G.Toussaint, Some constrained minimax and maximin
location problems, Studies in Locational Analysis, 15 (2000), 17-35.
[4] Klamroth, K., Single-Facility Location Problems with Barriers, Springer,
2002.
[5] S.Nickel & J.Puerto, Location theory: A unified approach. Springer,
2005.
[6] Y.Ohsawa, F.Plastria, K.Tamura, Euclidean push-pull partial covering
problems, Computers and Operations Research, Volume 33 (12), 2006, 3566-3582.
[7] F.Plastria, Continuous location problems, Chapter 11 in Drezner (Ed.),
Facility Location: a survey of applications and methods, Springer 1995, 229-266.
[8] F.Plastria, Continuous covering location problems, in H.Hamacher and
Z.Drezner (eds.), Location Analysis: Theory and Applications, Springer, 2001,
Chapter 2, 39-83.
[9] F.Plastria, Asymmetric distances, semidirected networks and majority in
Fermat-Weber problems, Locator: ePublication of Location Analysis, 2 (2001)
15-62.
[10] F.Plastria, Location = distances and optimisation, Publications du
Département de Mathématique, FUNDP, Namur, Belgium, Report 2003/04, May 2003,
60p.
[11] F.Plastria & E.Carrizosa, Optimal location and design of a competitive
facility, Mathematical Programming 100, 2004, 247-265.
[12] F.Plastria, Avoiding cannibalisation and/or competitor reaction in planar
single facility location, Journal of the Operational Research Society of Japan,
48 (2), 2005, 148-157.