Inequality measures for location problems.

*(English)*Zbl 0923.90101Summary: We consider the measurement of inequality in the distribution of distances between the users and the facility to be located. We provide a general framework for quantifying inequality, which is based on the notion of proximity between a proposed solution and a set of ideal solutions. Many inequality measures used in the location literature (and some that have not been used) can be derived from this general framework. We present some fundamental axioms for the measurement of inequality, and show that only two of the measures considered satisfy these axioms. As a result of a computational experiment, we find that there is considerable agreement (as to which solution is the best) between these two measures, however, the agreement is not complete. We discuss reasons for disagreements, and properties of these measures when applied to location problems. We provide some practical suggestions for modeling inequality in a location problem and give directions for future research.

##### MSC:

90B80 | Discrete location and assignment |