Research

Research directions of Project FLO

  • Location problems with restrictions and non-convex location problems
  • Multi-facility location problems and approximation problems
  • Location problems with uncertainties in the data
  • Creating algorithms for solving uncertain multiobjective location problems taking into account different robustness concepts.
  • Studying extended multiobjective location problems

Please also see our lists of research publications and presentations.

Additionally, FLO uses developments from the following fields of research:

Location Theory

Location problems appear in many variants and with different constraints depending on the application. Location problems arise in urban development and regional planning as well as in engineering, economics and radiotherapy treatment.

Some recommended books:

A. Göpfert, T. Riedrich and Chr. Tammer: Angewandte Funktionalanalysis – Motivationen und Methoden für Mathematiker und Wirtschaftswissenschaftler, Vieweg+Teubner, Wiesbaden, 2009

H.W. Hamacher, K. Klamroth and Chr. Tammer : Standortoptimierung. In: Luderer, B. (Ed.): Die Kunst des Modellierens. Mathematisch-ökonomische Modelle (S. 139-156), Teubner-Verlag, 2008

Z. Drezner and  H.W. Hamacher : Facility Location: Theory and Algorithms, Springer, Berlin, 2001

H. W. Hamacher : Mathematische Lösungsverfahren für planare Standortprobleme, Vieweg Verlag, 1995

R. F. Love, J. G. Morris and G. O. Wesolowsky : Facility Location: Models and Methods, North Holland, New York, 1988

Vector Optimization

In vector optimization, one investigates optimization problems with a vector-valued objective function. Fundamental works concerning vector optimization date back to F. Y. Edgeworth (1881) und V. Pareto (1896).

Some recommended books:

G. Eichfelder : Variable Ordering Structures in Vector Optimization,
Springer, 2014

A. Löhne : Vector Optimization with Infimum and Supremum, Springer, 2011

J. Jahn : Vector Optimization – Theory, Applications, and Extensions, Springer, Berlin, 2nd Edition, 2011

A. Göpfert, H. Riahi, Chr. Tammer and C. Zălinescu : Variational Methods in Partially Ordered Spaces, CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 17, Springer-Verlag, New York, 2003

Set-valued Optimization and Uncertain Optimization

Some recommended books:

A. A. Khan, Chr. Tammer and C. Zălinescu : Set-valued Optimization: An Introduction with Applications, Springer, 2015

A. Ben-Tal, L. Ghaoui and A. Nemirovski : Robust Optimization, Princeton University Press, 2009