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.

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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.

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Purpose Motivated by the increasing need to provide support to refugees, which remains as a pressing issue in the agenda of many countries, the purpose of this paper is to consider the refugee camp management problem. Although each of these countries may have different procedures shaped by their own culture, rules and regulations, the main structure of the problem can be modeled utilizing a general framework which will apply to different practices. Design/methodology/approach In this study, the authors consider the issue with an operations research (OR) perspective and provide such a framework utilizing Turkish Red Crescent (TRC)’s field expertise in many regions of the world. In the proposed framework, the overall refugee camp management problem is first categorized in two main phases: the establishment phase, which consists of one-time decisions like infrastructure design and the administration phase, which focuses on routine decisions that are taken on a periodic basis like aid distribution. Findings The authors then provide a unifying decision-making model for the establishment phase and detail the administrative phase via subcategories, linking the relevant problems to the OR literature. The proposed framework is general enough to be used by practitioners and to be utilized by the academicians to define new OR problems to the literature. Originality/value TRC’s know-how is very broad and extensive. Integrating that know-how with OR perspective, the authors provide a general framework that could be of use to practitioners as well as academicians. The proposed framework will constitute an example for countries of asylum and national or international NGOs to manage the refugee camps efficiently. The authors also highlight main challenges and dynamics of the decision-making problems encountered in different parts of the proposed framework, which may constitute many different problems to the OR literature each of which can open new venues for future research.