Incorporating balance concerns in resource allocation decisions: A bi-criteria modelling approach

Abstract

We consider resource allocation problems where inputs are allocated to di¤erent entities such as activities, projects or departments. In such problems a common goal is achieving a desired balance in the allocation over di¤erent categories of the entities. We propose a bi-criteria framework for trading balance o¤ against e¢ ciency. We de…ne and categorize indicators based on balance distribution and propose formulations and solution algorithms which provide insight into the balance-e¢ ciency tradeo¤. We illustrate our models by applying them to the data of a portfolio selection problem faced by a science funding agency and to randomly generated large-sized problem instances to demonstrate computational feasibility.

Carbon Emissions Abatement (CEA) allocation and compensation schemes based on DEA

“…And likewise, the proposed model aides in the analyses of trade-offs among the 3E objectives. Recently, Karsu and Morton [29] provided a bi-criteria framework to trade balance off against efficiency in resource allocation problems, in which the equality criterion can be deemed as a special case of the balance criterion.…”

Inequity averse optimization in operational research

“…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), …”

“…Bollapragada and Garbiras (2004) propose a mathematical model for this problem, in which balance concerns over clients are also considered. Similarly, Karsu and Morton (2014) propose a bicriteria modeling framework that considers both efficiency and balance concerns in resource allocation problems.…”

“…In a restaurant revenue management problem (Bertsimas & Shioda, 2003) ensure equity across customers of the same size by using constraints that seat them on a FCFS basis. Karsu and Morton (2014) propose a two dimensional framework to trade balance off against efficiency in resource allocation problems motivated by problems in R&D project selection. They use imbalance indices which measure the deviation of an allocation from an ideally balanced allocation the DM provides.…”

Balancing the costs of human resources on an ERP project

“…A balanced project team is instrumental to any project [21,26,27] and must be assembled from the most knowledgeable employees in order to accomplish the required transformation [4]. However, an ERP project can rarely be completed by company personnel alone and requires consulting support [28,29].…”