A Unified Framework for Analyzing and Optimizing a Class of Convex Fairness Measures

References

• Abul Naga RH, Yalcin T (2008) Inequality measurement for ordered response health data. J. Health Econom. 27(6):1614–1625.Crossref, Google Scholar
• Ahmadi-Javid A, Seyedi P, Syam SS (2017) A survey of healthcare facility location. Comput. Oper. Res. 79:223–263.Crossref, Google Scholar
• Andreoli F, Zoli C (2020) From unidimensional to multidimensional inequality: A review. Metron 78(1):5–42.Crossref, Google Scholar
• Armbruster B, Delage E (2015) Decision making under uncertainty when preference information is incomplete. Management Sci. 61(1):111–128.Link, Google Scholar
• Atkinson AB (1975) Economics of Inequality (Clarendon Press, New York).Google Scholar
• Barbati M, Piccolo C (2016) Equality measures properties for location problems. Optim. Lett. 10(5):903–920.Crossref, Google Scholar
• Bateni M, Chen Y, Ciocan DF, Mirrokni V (2022) Fair resource allocation in a volatile marketplace. Oper. Res. 70(1):288–308.Link, Google Scholar
• Bertsimas D, Shtern S (2018) A scalable algorithm for two-stage adaptive linear optimization. Preprint, submitted July 8, https://arxiv.org/abs/1807.02812.Google Scholar
• Bertsimas D, Farias VF, Trichakis N (2012) On the efficiency-fairness trade-off. Management Sci. 58(12):2234–2250.Link, Google Scholar
• Bertsimas D, Farias VF, Trichakis N (2013) Fairness, efficiency, and flexibility in organ allocation for kidney transplantation. Oper. Res. 61(1):73–87.Link, Google Scholar
• Breugem T, Dollevoet T, Huisman D (2022) Is equality always desirable? Analyzing the trade-off between fairness and attractiveness in crew rostering. Management Sci. 68(4):2619–2641.Link, Google Scholar
• Celik Turkoglu D, Erol Genevois M (2020) A comparative survey of service facility location problems. Ann. Oper. Res. 292(1):399–468.Crossref, Google Scholar
• Chakravarty SR (1999) Measuring inequality: The axiomatic approach. Samuels WJ, Darity W Jr, eds. Handbook of Income Inequality Measurement (Springer, New York), 163–186.Crossref, Google Scholar
• Chakravarty SR (2007) A deprivation-based axiomatic characterization of the absolute Bonferroni index of inequality. J. Econom. Inequality 5(3):339–351.Crossref, Google Scholar
• Chang D, Lin M, Zhang C (2018) On the generalization ability of online gradient descent algorithm under the quadratic growth condition. IEEE Trans. Neural Networks Learning Systems 29(10):5008–5019.Crossref, Google Scholar
• Chen VX, Hooker J (2023) A guide to formulating fairness in an optimization model. Ann. Oper. Res. 326(1):581–619.Crossref, Google Scholar
• Cowell FA (2000) Measurement of inequality. Atkinson AB, Bourguignon F, eds. Handbook of Income Distribution, vol. 1 (North Holland, Amsterdam), 87–166.Crossref, Google Scholar
• Cowell FA (2011) Measuring Inequality (Oxford University Press, New York).Crossref, Google Scholar
• Cowell FA, Kuga K (1981) Inequality measurement: An axiomatic approach. Eur. Econom. Rev. 15(3):287–305.Crossref, Google Scholar
• Csiszar O (2021) Ordered weighted averaging operators: A short review. IEEE Systems Man Cybernetics Magazine 7(2):4–12.Crossref, Google Scholar
• Dalton H (1920) The measurement of the inequality of incomes. Econom. J. 30(119):348–361.Google Scholar
• Daskin MS (2013) Network and Discrete Location: Models, Algorithms, and Applications, 2nd ed. (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
• Diakonikolas J, Fazel M, Orecchia L (2020) Fair packing and covering on a relative scale. SIAM J. Optim. 30(4):3284–3314.Crossref, Google Scholar
• Donaldson D, Weymark JA (1980) A single-parameter generalization of the Gini indices of inequality. J. Econom. Theory 22(1):67–86.Crossref, Google Scholar
• Dönmez Z, Ayyıldız M, Uslu B, Karsu O, Kara BY (2023) Fairness in humanitarian logistics: State of the art and future directions. Preprint, submitted April 5, https://doi.org/10.2139/ssrn.4396254.Google Scholar
• Filippi C, Guastaroba G, Speranza MG (2021) On single-source capacitated facility location with cost and fairness objectives. Eur. J. Oper. Res. 289(3):959–974.Crossref, Google Scholar
• Foster JE (1983) An axiomatic characterization of the Theil measure of income inequality. J. Econom. Theory 31(1):105–121.Crossref, Google Scholar
• Gini C (1912) Variabilità e Mutabilità: Contributo Allo Studio Delle Distribuzioni e Delle Relazioni Statistiche (Cuppini, Bologna, Italy).Google Scholar
• Gutjahr WJ, Fischer S (2018) Equity and deprivation costs in humanitarian logistics. Eur. J. Oper. Res. 270(1):185–197.Crossref, Google Scholar
• Hooker JN, Williams HP (2012) Combining equity and utilitarianism in a mathematical programming model. Management Sci. 58(9):1682–1693.Link, Google Scholar
• Hu J, Bansal M, Mehrotra S (2018) Robust decision making using a general utility set. Eur. J. Oper. Res. 269(2):699–714.Crossref, Google Scholar
• Jagtenberg CJ, Mason AJ (2020) Improving fairness in ambulance planning by time sharing. Eur. J. Oper. Res. 280(3):1095–1107.Crossref, Google Scholar
• Jancewicz B (2016) Income inequalities: Axioms of income inequality measures and people’s perceptions. Decyzje 13(25):21–42.Crossref, Google Scholar
• Kakade SM, Tewari A (2008) On the generalization ability of online strongly convex programming algorithms. Koller D, Schuurmans D, Bengio Y, Bottou L, eds. NIPS’08: Proc. 22nd Internat. Conf. Neural Inform. Processing Systems (Curran Associates, Inc., Red Hook, NY), 801–808.Google Scholar
• Kakwani N (1980) On a class of poverty measures. Econometrica 48(2):437–446.Crossref, Google Scholar
• Karsu Ö, Morton A (2015) Inequity averse optimization in operational research. Eur. J. Oper. Res. 245(2):343–359.Crossref, Google Scholar
• Kolm SC (1976) Unequal inequalities. I. J. Econom. Theory 12(3):416–442.Crossref, Google Scholar
• Kostreva MM, Ogryczak W, Wierzbicki A (2004) Equitable aggregations and multiple criteria analysis. Eur. J. Oper. Res. 158(2):362–377.Crossref, Google Scholar
• Lan T, Kao D, Chiang M, Sabharwal A (2010) An axiomatic theory of fairness in network resource allocation. 2010 Proc. IEEE INFOCOM (IEEE, Piscataway, NJ), 1–9.Google Scholar
• Lejeune MA, Turner J (2019) Planning online advertising using Gini indices. Oper. Res. 67(5):1222–1245.Link, Google Scholar
• Lewis EO, MacKenzie D, Kaminsky J (2021) Exploring equity: How equity norms have been applied implicitly and explicitly in transportation research and practice. Transportation Res. Interdisciplinary Perspect. 9:100332.Crossref, Google Scholar
• Li H, Delage E, Zhu N, Pinedo M, Ma S (2024) Distributional robustness and inequity mitigation in disaster preparedness of humanitarian operations. Manufacturing Service Oper. Management 26(1):197–214.Link, Google Scholar
• Liu Y, Pichler A, Xu H (2019) Discrete approximation and quantification in distributionally robust optimization. Math. Oper. Res. 44(1):19–37.Abstract, Google Scholar
• Marsh MT, Schilling DA (1994) Equity measurement in facility location analysis: A review and framework. Eur. J. Oper. Res. 74(1):1–17.Crossref, Google Scholar
• Marshall AW, Olkin I, Arnold BC (2011) Inequalities: Theory of Majorization and Its Applications (Springer, New York).Crossref, Google Scholar
• Marynissen J, Demeulemeester E (2019) Literature review on multi-appointment scheduling problems in hospitals. Eur. J. Oper. Res. 272(2):407–419.Crossref, Google Scholar
• Mehran F (1976) Linear measures of income inequality. Econometrica 44(4):805–809.Crossref, Google Scholar
• Mo J, Walrand J (2000) Fair end-to-end window-based congestion control. IEEE/ACM Trans. Networking 8(5):556–567.Crossref, Google Scholar
• Mostajabdaveh M, Gutjahr WJ, Sibel Salman F (2019) Inequity-averse shelter location for disaster preparedness. IISE Trans. 51(8):809–829.Crossref, Google Scholar
• Moulin H (2004) Fair Division and Collective Welfare (MIT Press, Cambridge, MA).Google Scholar
• Mussard S, Mornet P (2019) A note on α-Gini measures. Rev. Income Wealth 65(3):675–682.Crossref, Google Scholar
• Nickel S, Puerto J (2006) Location Theory: A Unified Approach (Springer Science & Business Media, Berlin, Heidelberg).Google Scholar
• Ogryczak W (2000) Inequality measures and equitable approaches to location problems. Eur. J. Oper. Res. 122(2):374–391.Crossref, Google Scholar
• Ogryczak W, Śliwiński T (2006) On direct methods for lexicographic min-max optimization. Gavrilova M, Gervasi O, Kumar V, Tan CK, Taniar D, Laganà A, Mun Y, Choo H, eds. Internat. Conf. Comput. Sci. Its Appl., Lecture Notes in Computer Science, vol. 3982 (Springer, Berlin, Heidelberg), 802–811.Google Scholar
• Pichler A, Xu H (2018) Quantitative stability analysis for minimax distributionally robust risk optimization. Math. Programming 191(1):47–77.Crossref, Google Scholar
• Rahmattalabi A, Vayanos P, Dullerud K, Rice E (2022) Learning resource allocation policies from observational data with an application to homeless services delivery. 2022 ACM Conf. Fairness Accountability Transparency (ACM Press, New York), 1240–1256.Google Scholar
• Rawls J (1999) A Theory of Justice, revised ed. (Harvard University Press, Cambridge, MA).Crossref, Google Scholar
• Shalev-Shwartz S, Zhang T (2012) Proximal stochastic dual coordinate ascent. Preprint, submitted November 12, https://arxiv.org/abs/1211.2717.Google Scholar
• Shapiro A (1994) Quantitative stability in stochastic programming. Math. Programming 67(1):99–108.Crossref, Google Scholar
• Shehadeh KS, Snyder LV (2023) Equity in stochastic healthcare facility location. Eiselt HA, Marianov V, eds. Uncertainty in Facility Location Problems, International Series in Operations Research & Management Science, vol. 347 (Springer, Cham, Switzerland), 303–334.Crossref, Google Scholar
• Shen S, Qian J, Cheng D, Yang K, Zhang G (2019) A sum-utility maximization approach for fairness resource allocation in wireless powered body area networks. IEEE Access 7:20014–20022.Crossref, Google Scholar
• Stȩpniak C (2007) An effective characterization of Schur-convex functions with applications. J. Convex Anal. 14(1):103–108.Google Scholar
• Sun L, Xie W, Witten T (2023) Distributionally robust fair transit resource allocation during a pandemic. Transportation Sci. 57(4):954–978.Link, Google Scholar
• Sun L, Deng H, Wei P, Xie W (2025) On a fair and risk-averse urban air mobility resource allocation problem under demand and capacity uncertainties. Naval Res. Logist. 72(1):111–132.Crossref, Google Scholar
• Theil H (1967) Economics and Information Theory (North-Holland, Amsterdam).Google Scholar
• Thon D (1982) An axiomatization of the Gini coefficient. Math. Soc. Sci. 2(2):131–143.Crossref, Google Scholar
• Uhde A, Schlicker N, Wallach DP, Hassenzahl M (2020) Fairness and decision-making in collaborative shift scheduling systems. Proc. 2020 CHI Conf. Human Factors Comput. Systems (ACM Press, New York), 1–13.Google Scholar
• Williams A, Cookson R (2000) Equity in health. Culyer AJ, Newhouse JP, eds. Handbook of Health Economics, Handbooks in Economics (Elsevier, Amsterdam), 1863–1910.Google Scholar
• Williamson R, Menon A (2019) Fairness risk measures. Chaudhuri K, Salakhutdinov R, eds. Proc. 36th Internat. Conf. Machine Learning, Proceedings of Machine Learning Research, vol. 97 (ML Research Press, Maastricht University, Maastricht, Netherlands), 6786–6797.Google Scholar
• Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Systems Man Cybernetics 18(1):183–190.Crossref, Google Scholar
• Zhang J, Liu Y, Yu G, Shen ZJ (2021) Robustifying humanitarian relief systems against travel time uncertainty. Naval Res. Logist. 68(7):871–885.Crossref, Google Scholar