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The Price of Imposing Vertical Equity Through Asymmetric Outcome Constraints

Author

Listed:
  • Thomas Breugem

    (Technology and Operations Management, INSEAD, Fontainebleau 77300, France)

  • Luk N. Van Wassenhove

    (Technology and Operations Management, INSEAD, Fontainebleau 77300, France)

Abstract

Vertical equity or fairness is an important aspect in many settings, yet has received relatively little attention in the literature. Recent developments underline the practical relevance (e.g., COVID-19 vaccination policies). It plays an important role in the performance evaluation of many (nongovernmental) organizations. For example, donors might require a family-planning organization to allocate a minimum fraction of the total utility (client volume) to a particular player (the “high-impact” subgroup of the population, e.g., young and poor clients). However, the price (decrease in client volume) of such requirements is not well-understood. Consequently, this price is not accounted for in decision making. We provide an analytical upper bound on the price (i.e., loss of overall utility) of vertical equity considerations in resource allocation. We assume that these concerns are expressed via outcome constraints, specifying a minimum percentage of the total utility for each player. Our set-up considers a decision maker maximizing total utility over a general convex set, subject to outcome constraints. The set-up is general and applicable to many practical problems. Our results depend only on high-level parameters and are therefore well-suited for strategic decision making. We conclude with two applications. First, we apply our results to practical instances in health delivery. We confirm that outcome constraints can entail a substantial price and analyze the factors driving this price close to the worst-case bound. Second, we analyze how our results can help bound the impact of prioritization in vaccine allocation.

Suggested Citation

  • Thomas Breugem & Luk N. Van Wassenhove, 2022. "The Price of Imposing Vertical Equity Through Asymmetric Outcome Constraints," Management Science, INFORMS, vol. 68(11), pages 7977-7993, November.
    • Handle: RePEc:inm:ormnsc:v:68:y:2022:i:11:p:7977-7993
    DOI: 10.1287/mnsc.2021.4287
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    References listed on IDEAS

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    1. 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.
    2. Ohad Eisenhandler & Michal Tzur, 2019. "The Humanitarian Pickup and Distribution Problem," Operations Research, INFORMS, vol. 67(1), pages 10-32, January.
    3. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    4. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    5. Cynthia Barnhart & Dimitris Bertsimas & Constantine Caramanis & Douglas Fearing, 2012. "Equitable and Efficient Coordination in Traffic Flow Management," Transportation Science, INFORMS, vol. 46(2), pages 262-280, May.
    6. Jessica H. McCoy & Hau L. Lee, 2014. "Using Fairness Models to Improve Equity in Health Delivery Fleet Management," Production and Operations Management, Production and Operations Management Society, vol. 23(6), pages 965-977, June.
    7. Marsh, Michael T. & Schilling, David A., 1994. "Equity measurement in facility location analysis: A review and framework," European Journal of Operational Research, Elsevier, vol. 74(1), pages 1-17, April.
    8. Nishi, Tatsushi & Sugiyama, Taichi & Inuiguchi, Masahiro, 2014. "Two-level decomposition algorithm for crew rostering problems with fair working condition," European Journal of Operational Research, Elsevier, vol. 237(2), pages 465-473.
    9. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2011. "The Price of Fairness," Operations Research, INFORMS, vol. 59(1), pages 17-31, February.
    10. John P. Dickerson & Ariel D. Procaccia & Tuomas Sandholm, 2019. "Failure-Aware Kidney Exchange," Management Science, INFORMS, vol. 65(4), pages 1768-1791, April.
    11. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2013. "Fairness, Efficiency, and Flexibility in Organ Allocation for Kidney Transplantation," Operations Research, INFORMS, vol. 61(1), pages 73-87, February.
    12. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2012. "On the Efficiency-Fairness Trade-off," Management Science, INFORMS, vol. 58(12), pages 2234-2250, December.
    13. Alexandre Jacquillat & Vikrant Vaze, 2018. "Interairline Equity in Airport Scheduling Interventions," Transportation Science, INFORMS, vol. 52(4), pages 941-964, August.
    14. Núñez Ares, José & de Vries, Harwin & Huisman, Dennis, 2016. "A column generation approach for locating roadside clinics in Africa based on effectiveness and equity," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1002-1016.
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