The Quintile Share Ratio in location analysis

The Quintile Share Ratio in location analysis

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Article ID: iaor20141819
Volume: 238
Issue: 1
Start Page Number: 166
End Page Number: 174
Publication Date: Oct 2014
Journal: European Journal of Operational Research
Authors: , ,
Keywords: inequality problems
Abstract:

The inequality measure ‘Quintile Share Ratio’ (QSR or sometimes S80/S20) is the primary income inequality measure in the European Union’s set of indicators on social cohesion. An important reason for its adoption as a leading indicator is its simplicity. The Quintile Share Ratio is ‘The ratio of total income received by the 20% of the population with the highest income (top quintile) to that received by the 20% of the population with the lowest income (lowest quintile)’. The QSR concept is used in this paper in the context of obnoxious facility location where the inequality is in distances to the obnoxious facility. The single facility location problem minimizing the QSR is investigated. The problem is investigated for continuous uniform demand in an area such as a disk, a rectangle, and a line; when demand is generated at a finite set of demand points; and when the facility can be located anywhere on a network. Optimal solution algorithms are devised for demand originating at a finite set of demand points and at nodes of the network. Computational experiments demonstrate the effectiveness of the algorithms.

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