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Combining Equity and Utilitarianism in a Mathematical Programming Model

Author

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  • J. N. Hooker

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • H. P. Williams

    (Department of Management, London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

Abstract

We discuss the problem of combining the conflicting objectives of equity and utilitarianism, for social policy making, in a single mathematical programming model. The definition of equity we use is the Rawlsian one of maximizing the minimum utility over individuals or classes of individuals. However, when the disparity of utility becomes too great, the objective becomes progressively utilitarian. Such a model is particularly applicable not only to health provision but to other areas as well. Building a mixed-integer/linear programming (MILP) formulation of the problem raises technical issues, because the objective function is nonconvex and the hypograph is not MILP representable in its initial form. We present a succinct formulation and show that it is "sharp" in the sense that its linear programming relaxation describes the convex hull of the feasible set (before extra resource allocation or policy constraints are added). We apply the formulation to a healthcare planning problem and show that instances of realistic size are easily solved by standard MILP software. This paper was accepted by Dimitris Bertsimas, optimization.

Suggested Citation

  • J. N. Hooker & H. P. Williams, 2012. "Combining Equity and Utilitarianism in a Mathematical Programming Model," Management Science, INFORMS, vol. 58(9), pages 1682-1693, September.
    • Handle: RePEc:inm:ormnsc:v:58:y:2012:i:9:p:1682-1693
    DOI: 10.1287/mnsc.1120.1515
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    References listed on IDEAS

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    16. Zhou, Liping & Geng, Na & Jiang, Zhibin & Wang, Xiuxian, 2018. "Multi-objective capacity allocation of hospital wards combining revenue and equity," Omega, Elsevier, vol. 81(C), pages 220-233.
    17. Satoshi Nakano & Kazuhiko Nishimura, 2016. "Optimal Population in a Finite Horizon," Papers 1608.01535, arXiv.org, revised Jan 2018.
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