The equitable dispersion problem

Most optimization problems focus on efficiency-based objectives. Given the increasing awareness of system inequity resulting from solely pursuing efficiency, we conceptualize a number of new element-based equity-oriented measures in the dispersion context. We propose the equitable dispersion problem that maximizes the equity among elements based on the introduced measures in a system defined by inter-element distances. Given the proposed optimization framework, we develop corresponding mathematical programming formulations as well as their mixed-integer linear reformulations. We also discuss computational complexity issues, related graph-theoretic interpretations and provide some preliminary computational results.