An Exact Method for Balancing Efficiency and Equity in the Liver Allocation Hierarchy

Abstract

We study the problem of (re)designing the regional network by which cadaveric livers are allocated. Whereas prior research focused mainly on maximizing a measure of efficiency of the network that was based on aggregate patient survival, we explicitly account for the trade-off between efficiency and a measure of geographical equity in the allocation process. To this end, we extend earlier optimization models to incorporate both objectives and develop an exact branch-and-price approach to solve this problem, generalizing a solution approach studied for the case where only efficiency is taken into account. In addition, we propose an effective solution algorithm that approximates the (generally nonconcave) frontier of Pareto-efficient solutions with respect to the two objectives by simultaneously generating and successively improving upper and lower bounds on this frontier. We implement and test our approach on observed data and show that solutions significantly dominating the current configuration in both efficiency and equity can be found. Of course, other subjective criteria are needed to choose among the different Pareto-efficient candidate solutions.

Redesigning Organ Allocation Boundaries for Liver Transplantation in the United States

“…Our model extends a handful of studies [11, 14, 16, 17] that investigate optimal boundaries for organ allocation using a mathematical approach. Most previous models [14, 16, 17] are based on a set covering mathematical formulation of which feasible sets are represented by all possible regional configurations resulting from different clusters of OPOs.…”

“…Most previous models [14, 16, 17] are based on a set covering mathematical formulation of which feasible sets are represented by all possible regional configurations resulting from different clusters of OPOs. This approach tends to be computationally very demanding.…”

“…First, it would be interesting to explore different equity measure definitions both for Model 1 and Model 2 in order to take into account additional aspects such as those considered by Kong et al [14] and by Demirci et al [16]. We are also interested in exploring the possibility of adapting our Model 2 to solve the problem of clustering the OPOs into UNOS regions so that the final allocation system represents the hierarchical system as presently implemented.…”

Inequity averse optimization in operational research

“…Applications include bandwidth or channel allocation (Tomaszewski, 2005;Lee et al, 2004;Lee & Cho, 2007;Luss, 2008;Salles & Barria, 2008;Ogryczak et al, 2008;Luss, 2010;Luss, 2012a;Jeong et al, 2005;Chang et al, 2006;Zukerman et al, 2008;Morell et al, 2008;Zhang & Ansari, 2010;Bonald et al, 2006;Heikkinen, 2004;Ogryczak et al, 2005;Kunqi et al, 2007), water rights allocation (Udías et al, 2012), health care planning (Earnshaw et al, 2007;Demirci et al, 2012;Hooker & Williams, 2012;Bertsimas et al, 2013), WIP (Kanban) allocation in production systems (Ryan & Vorasayan, 2005), fixed cost allocation (Li et al, 2013;Butler & Williams, 2006), and public resource allocation such as allocating voting machines to election precincts . There are also studies that consider general resource allocation settings such as Bertsimas et al (2011), Hooker (2010, Nace and Orlin (2007), Medernach and Sanlaville (2012) and Bertsimas et al (2014).…”

“…Bertsimas et al (2014) propose a modeling framework for general dynamic resource allocation Table 2 Classical problems in OR re-considered with equity concerns. Tomaszewski (2005), Lee, Moon, and Cho (2004), Lee and Cho (2007), Luss (2008), Salles and Barria (2008), Ogryczak, Wierzbicki, and Milewski (2008), Luss (2010), Luss (2012a), Jeong, Kim, and Lee (2005), Chang, Lee, and Kim (2006), Zukerman, Mammadov, Tan, Ouveysi, and Andrew (2008), Morell, Seco-Granados, and Vázquez-Castro (2008), Zhang and Ansari (2010), Bonald, Massoulié, Proutière, andVirtamo (2006), Heikkinen (2004), Ogryczak, Pioro, and Tomaszewski (2005), Udías, Ríos Insua, Cano, and Fellag (2012), Earnshaw, Hicks, Richter, and Honeycutt (2007), Demirci, Schaefer, Romeijn, and Roberts (2012), Hooker and Williams (2012), Bertsimas, Farias, and Trichakis (2013), Ryan and Vorasayan (2005), Li, Yang, Chen, Dai, and Liang (2013), Butler and Williams (2006), Yang, Allen, Fry, and Kelton (2013), Trichakis (2011), Bertsimas, Farias, andTrichakis (2012), Hooker (2010), Nace and Orlin (2007), Medernach and Sanlaville (2012), Bertsimas, Gupta, and Lulli (2014), Karsu and Morton (2014), Johnson, Turcotte, and Sullivan (2010), Kozanidis (2009), Eiselt and Marianov (2008), Vossen and Ball (2006), …”