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Journal of Applied Mathematics
Volume 2014, Article ID 612018, 25 pages
Review Article

Fair Optimization and Networks: A Survey

1Institute of Control and Computation Engineering, Warsaw University of Technology, 00-665 Warsaw, Poland
2Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA
3Department of Electrical and Information Technology, Lund University, 22100 Lund, Sweden
4Institute of Telecommunications, Warsaw University of Technology, 00-665 Warsaw, Poland
5Laboratoire Heudiasyc, Université de Technologie de Compiègne, 60203 Compiègne, France

Received 7 March 2014; Revised 3 August 2014; Accepted 6 August 2014; Published 3 September 2014

Academic Editor: Yuri N. Sotskov

Copyright © 2014 Wlodzimierz Ogryczak et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Optimization models related to designing and operating complex systems are mainly focused on some efficiency metrics such as response time, queue length, throughput, and cost. However, in systems which serve many entities there is also a need for respecting fairness: each system entity ought to be provided with an adequate share of the system’s services. Still, due to system operations-dependant constraints, fair treatment of the entities does not directly imply that each of them is assigned equal amount of the services. That leads to concepts of fair optimization expressed by the equitable models that represent inequality averse optimization rather than strict inequality minimization; a particular widely applied example of that concept is the so-called lexicographic maximin optimization (max-min fairness). The fair optimization methodology delivers a variety of techniques to generate fair and efficient solutions. This paper reviews fair optimization models and methods applied to systems that are based on some kind of network of connections and dependencies, especially, fair optimization methods for the location problems and for the resource allocation problems in communication networks.