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The equitable dispersion problem

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  • Prokopyev, Oleg A.
  • Kong, Nan
  • Martinez-Torres, Dayna L.

Abstract

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.

Suggested Citation

  • Prokopyev, Oleg A. & Kong, Nan & Martinez-Torres, Dayna L., 2009. "The equitable dispersion problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 59-67, August.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:1:p:59-67
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    Cited by:

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    3. Sayyady, Fatemeh & Fathi, Yahya, 2016. "An integer programming approach for solving the p-dispersion problem," European Journal of Operational Research, Elsevier, vol. 253(1), pages 216-225.
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    5. Martí, Rafael & Martínez-Gavara, Anna & Pérez-Peló, Sergio & Sánchez-Oro, Jesús, 2022. "A review on discrete diversity and dispersion maximization from an OR perspective," European Journal of Operational Research, Elsevier, vol. 299(3), pages 795-813.
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    15. Z. Wu & G. Li & J. Quan, 2011. "Global optimality conditions and optimization methods for quadratic integer programming problems," Journal of Global Optimization, Springer, vol. 51(3), pages 549-568, November.
    16. Lei, Ting L. & Church, Richard L., 2015. "On the unified dispersion problem: Efficient formulations and exact algorithms," European Journal of Operational Research, Elsevier, vol. 241(3), pages 622-630.
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    21. San Segundo, Pablo & Coniglio, Stefano & Furini, Fabio & Ljubić, Ivana, 2019. "A new branch-and-bound algorithm for the maximum edge-weighted clique problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 76-90.
    22. Amirgaliyeva, Zhazira & Mladenović, Nenad & Todosijević, Raca & Urošević, Dragan, 2017. "Solving the maximum min-sum dispersion by alternating formulations of two different problems," European Journal of Operational Research, Elsevier, vol. 260(2), pages 444-459.
    23. Gliesch, Alex & Ritt, Marcus, 2021. "A hybrid heuristic for the maximum dispersion problem," European Journal of Operational Research, Elsevier, vol. 288(3), pages 721-735.

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