Browsing by Subject "Equitable preferences"

Now showing 1 - 3 of 3

Open Access
Capturing preferences for inequality aversion in decision support
(Elsevier, 2018-01-16) Karsu, Özlem; Morton, A.; Argyris, N.
We investigate the situation where there is interest in ranking distributions (of income, of wealth, of health, of service levels) across a population, in which individuals are considered preferentially indistinguishable and where there is some limited information about social preferences. We use a natural dominance relation, generalised Lorenz dominance, used in welfare comparisons in economic theory. In some settings there may be additional information about preferences (for example, if there is policy statement that one distribution is preferred to another) and any dominance relation should respect such preferences. However, characterising this sort of conditional dominance relation (specifically, dominance with respect to the set of all symmetric increasing quasiconcave functions in line with given preference information) turns out to be computationally challenging. This challenge comes about because, through the assumption of symmetry, any one preference statement (“I prefer giving $100 to Jane and $110 to John over giving $150 to Jane and $90 to John”) implies a large number of other preference statements (“I prefer giving $110 to Jane and $100 to John over giving $150 to Jane and $90 to John”; “I prefer giving $100 to Jane and $110 to John over giving $90 to Jane and $150 to John”). We present theoretical results that help deal with these challenges and present tractable linear programming formulations for testing whether dominance holds between any given pair of distributions. We also propose an interactive decision support procedure for ranking a given set of distributions and demonstrate its performance through computational testing.
Open Access
Eşitlikçi çok amaçlı sırt çantası problemi
(Gazi Üniversitesi Fen Bilimleri Enstitüsü, 2018) Karsu, Özlem
Bu çalışmada, eşitlikçi kaygıların olduğu kaynak dağıtımı problemi için kullanılabilecek, çok amaçlı matematiksel modelleme yaklaşımı geliştirilmiştir. Karar vericinin eşitlikçi tercih ilişkisine sahip olduğu varsayılmış ve eşitlikçi Pareto çözümler bulunması amaçlanmıştır. Eşitlikçi Pareto çözüm kümesinin bulunması için, problemdeki eşitlikçi kaygıları gözönüne alarak tasarlanmış, eşitlikçi Pareto çözümler vermeyecek durum vektörlerini alt ve üst sınırlar kullanarak eleyen, bir dinamik programlama algoritması önerilmiştir. Bu algoritmada, yazında önerilen alt sınırlara ek olarak yeni bir alt sınır mekanizması kullanılmış ve etkililiği gösterilmiştir. Dinamik programlama algoritması, epsilon kısıt yöntemi ile iki amaçlı problemler için karşılaştırılmıştır. Ayrıca, üç amaçlı problemler için epsilon kısıt yöntemi sonuçları verilmiştir.
Open Access
Solution approaches for equitable multiobjective integer programming problems
(Springer, 2022-04) Bashir, Bashir; Karsu, Özlem
We consider multi-objective optimization problems where the decision maker (DM) has equity concerns. We assume that the preference model of the DM satisfies properties related to inequity-aversion, hence we focus on finding nondominated solutions in line with the properties of inequity-averse preferences, namely the equitably nondominated solutions. We discuss two algorithms for finding good subsets of equitably nondominated solutions. The first approach is an extension of an interactive approach developed for finding the most preferred nondominated solution when the utility function is assumed to be quasiconcave. We find the most preferred equitably nondominated solution when the utility function is assumed to be symmetric quasiconcave. In the second approach we generate an evenly distributed subset of the set of equitably nondominated solutions to be considered further by the DM. We show the computational feasibility of the two algorithms on equitable multi-objective knapsack problem, in which projects in different categories are to be funded subject to a limited budget. We perform experiments to show and discuss the performances of the algorithms. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.