Equity-Efficiency Bicriteria Location with Squared Euclidean Distances

Abstract

A facility has to be located within a given region taking two criteria of equity and efficiency into account. Equity is sought by minimizing the inequality in the inhabitant-facility distances, as measured by the sum of the absolute differences between all pairs of squared Euclidean distances from inhabitants to the facility. This measure meets the Pigou-Dalton condition of transfers, and can easily be minimized. Efficiency is measured through optimizing the sum of squared inhabitant-facility distances, either to be minimized or maximized for an attracting or repellent facility respectively. Geometric localization results are obtained for the whole set of Pareto optimal solutions for each of the two resulting bicriteria problems within a convex polygonal region. A polynomial procedure is developed to obtain the full bicriteria plot, both trade-off curves and the corresponding efficient sets.

Inequity averse optimization in operational research

“…Especially in essential public service facility location models, geographic equity of access to the service facilities is considered as one of the main requirements for an applicable solution. The access level can be measured in different terms such as the distance between demand points (customers) and the facilities (as in Batta et al, 2014;Maliszewski et al, 2012;Smith et al, 2013;Bell et al, 2011;Ohsawa et al, 2008;Chanta et al, 2011;Jia et al, 2007;Melachrinoudis & Xanthopulos, 2003;Ohsawa & Tamura, 2003;Mladenovic et al, 2003;López-de-los Mozos et al, 2013;Lejeune & Prasad, 2013) or the time required to access the facility from the demand points as in Mestre et al (2012) and Smith et al (2009). Ogryczak (2009) considers the generic location problem from a multicriteria perspective and formulates a model where each individual access level is minimized (see Table 2).…”

“…(5) Sum of pairwise (absolute) differences ( i∈I j∈J |y i − y j |): Sum of absolute differences between all pairs is considered in Ohsawa et al (2008), Al-Yakoob and Sherali (2006) and Lejeune and Prasad (2013) . Like the Gini coefficient and variance, this measure satisfies the PD.…”

Effectiveness–equity models for facility location problems on tree networks

“…Moreover, bicriteria models that have studied effectiveness-equity tradeoffs have either considered discrete location contexts [26] or used equity measures that do not satisfy the Principle of Transfers [18]. Location models have employed other equity measures that do satisfy the Principle of Transfers [36] but not necessarily in the context of examining tradeoffs with efficiency-one exception is the work of Ohsawa et al [33] who studied a bicriteria model for locations in a plane. Our proposed models extend this line of analysis when location is restricted to tree networks.…”

The multicriteria big cube small cube method

“…Hansen and Thisse (1981) propose a solution strategy for the bicriteria WeberRawls problem, and Hamacher and Nickel (1996) consider planar location problems where the objective functions are either Weber or center problems. Today, a wide range of multicriteria location problems with different objectives are reported, see, for example, Nickel et al (1997), Juel (1998a, 1998b), Melachrinoudis and Xanthopulos (2003), Blanquero and Carrizosa (2002), Skriver and Anderson (2003), Ohsawa (2000), Ohsawa and Tamura (2003), Ohsawa et al (2006Ohsawa et al ( , 2008. See Carrizosa and Plastria (1999) for a survey about semi-obnoxious facility location problems.…”