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Combining Equity and Utilitarianism in a Mathematical Programming Model

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... Full description

Journal Title: Management science 2012-09, Vol.58 (9), p.1682-1693
Main Author: HOOKER, J. N
Other Authors: WILLIAMS, H. P
Format: Electronic Article Electronic Article
Language: English
Subjects:
Publisher: Hanover, MD: INFORMS
ID: ISSN: 0025-1909
Link: http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26355540
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recordid: cdi_proquest_journals_1041256894
title: Combining Equity and Utilitarianism in a Mathematical Programming Model
format: Article
creator:
  • HOOKER, J. N
  • WILLIAMS, H. P
subjects:
  • applications
  • Applied sciences
  • Biological and medical sciences
  • Dialysis
  • Economy. Management
  • Equality
  • Equity
  • Exact sciences and technology
  • Health and social institutions
  • Health care industry
  • Health planning
  • healthcare
  • integer programming
  • Kidneys
  • Linear programming
  • Management science
  • Mathematical functions
  • Mathematical models
  • Mathematical programming
  • Medical sciences
  • Methods
  • mixed-integer modeling
  • Models
  • Operational research and scientific management
  • Operational research. Management science
  • Policy making
  • Programming models
  • Public health. Hygiene
  • Public health. Hygiene-occupational medicine
  • Resource allocation
  • Social policy
  • Social service
  • Social welfare
  • Studies
  • Utilitarianism
ispartof: Management science, 2012-09, Vol.58 (9), p.1682-1693
description: 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.
language: eng
source:
identifier: ISSN: 0025-1909
fulltext: no_fulltext
issn:
  • 0025-1909
  • 1526-5501
url: Link


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descriptionWe 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.
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subjectapplications ; Applied sciences ; Biological and medical sciences ; Dialysis ; Economy. Management ; Equality ; Equity ; Exact sciences and technology ; Health and social institutions ; Health care industry ; Health planning ; healthcare ; integer programming ; Kidneys ; Linear programming ; Management science ; Mathematical functions ; Mathematical models ; Mathematical programming ; Medical sciences ; Methods ; mixed-integer modeling ; Models ; Operational research and scientific management ; Operational research. Management science ; Policy making ; Programming models ; Public health. Hygiene ; Public health. Hygiene-occupational medicine ; Resource allocation ; Social policy ; Social service ; Social welfare ; Studies ; Utilitarianism
ispartofManagement science, 2012-09, Vol.58 (9), p.1682-1693
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abstractWe 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.
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