## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2014, Special Issue (2014), Article ID 612018, 25 pages.

### Fair Optimization and Networks: A Survey

Wlodzimierz Ogryczak, Hanan Luss, Michał Pióro, Dritan Nace, and Artur Tomaszewski

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#### Abstract

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.

#### Article information

**Source**

J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 612018, 25 pages.

**Dates**

First available in Project Euclid: 27 February 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1425050663

**Digital Object Identifier**

doi:10.1155/2014/612018

**Mathematical Reviews number (MathSciNet)**

MR3259214

#### Citation

Ogryczak, Wlodzimierz; Luss, Hanan; Pióro, Michał; Nace, Dritan; Tomaszewski, Artur. Fair Optimization and Networks: A Survey. J. Appl. Math. 2014, Special Issue (2014), Article ID 612018, 25 pages. doi:10.1155/2014/612018. https://projecteuclid.org/euclid.jam/1425050663

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Zentralblatt MATH: 1233.90212

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Zentralblatt MATH: 1180.90115

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Zentralblatt MATH: 0949.90047

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Zentralblatt MATH: 1176.90205

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