Effectiveness-equity models for facility location problems on tree networks

We propose models to investigate effectiveness-equity tradeoffs in tree network facility location problems. We use the commonly used median objective as a measure of effectiveness, and the Gini index as a measure of (in)equity, and formulate bicriteria problems involving these objectives. We develop procedures to identify an efficient set of solutions to these problems, analyze the complexity of the proposed procedures, and finally illustrate the procedures with an example.