Inequity averse optimization in operational research

Abstract

a b s t r a c tThere are many applications across a broad range of business problem domains in which equity is a concern and many well-known operational research (OR) problems such as knapsack, scheduling or assignment problems have been considered from an equity perspective. This shows that equity is both a technically interesting concept and a substantial practical concern. In this paper we review the operational research literature on inequity averse optimization. We focus on the cases where there is a tradeoff between efficiency and equity.We discuss two equity related concerns, namely equitability and balance. Equitability concerns are distinguished from balance concerns depending on whether an underlying anonymity assumption holds. From a modeling point of view, we classify three main approaches to handle equitability concerns: the first approach is based on a Rawlsian principle. The second approach uses an explicit inequality index in the mathematical model. The third approach uses equitable aggregation functions that can represent the DM's preferences, which take into account both efficiency and equity concerns. We also discuss the two main approaches to handle balance: the first approach is based on imbalance indicators, which measure deviation from a reference balanced solution. The second approach is based on scaling the distributions such that balance concerns turn into equitability concerns in the resulting distributions and then one of the approaches to handle equitability concerns can be applied.We briefly describe these approaches and provide a discussion of their advantages and disadvantages. We discuss future research directions focussing on decision support and robustness.

Eşitlikçi Çok Amaçlı Sırt Çantası Problemi

“…Problemin yazındaki klasik çok amaçlı problemlerden bir diğer farkı da, tercih ilişkisinin simetri özelliğidir, yani iki kategori arasında ayrım yapmayan bir karar verici için (3, 5) vektörü ile (5, 3) aynı derecede iyidir. Yazında, eşitlikçi kaygıların olduğu durumlarda odaklanılması gereken çözüm kümesinin eşitlikçi Pareto kümesi adı verilen bir çözüm kümesi olması gerektiği belirtilmektedir ( [6], [10]) . Dolayısıyla, eşitlikçi kesikli sırt çantası problemi, oluşturulan matematiksel modele klasik Pareto çözümler yerine eşitlikçi Pareto çözümler bulmayı amaçlar.…”

Price of Fairness for allocating a bounded resource

“…From a wider perspective, many authors have dealt with the problem of balancing global efficiency and fairness in terms of defining appropriate models or designing suitable objective functions or determining tradeoff solutions (see for instance [3,5,22]). A recent survey on the operations research literature that considers the tradeoff between efficiency and equity is [17].…”

Dual cone approach to convex-cone dominance in multiple criteria decision making

“…Linear programming is then used to check whether alternatives would lie in or under such dominance cones. See also, Prasad, Karwan, and Zionts (1997), Ramesh, Karwan, and Zionts (1988), Korhonen & Karaivanova (1999), and Karsu (2014).…”