Capturing preferences for inequality aversion in decision support

We investigate the situation where there is interest in ranking distributions (of income, of wealth, of health, of service levels) across a population, in which individuals are considered preferentially indistinguishable and where there is some limited information about social pref- erences. We use a natural dominance relation, generalized Lorenz dominance, used in welfare comparisons in economic theory. In some settings there may be additional information about preferences (for example, if there is policy statement that one distribution is preferred to an- other) and any dominance relation should respect such preferences. However, characterising this sort of conditional dominance relation (specifically, dominance with respect to the set of all symmetric increasing quasiconcave functions in line with given preference information) turns out to be computationally challenging. This challenge comes about because, through the as- sumption of symmetry, any one preference statement (“I prefer giving $100 to Jane and$110 to John over giving $150 to Jane and$90 to John”) implies a large number of other preference statements (“I prefer giving $110 to Jane and$100 to John over giving $150 to Jane and$90 to John”; “I prefer giving $100 to Jane and$110 to John over giving $90 to Jane and$150 to John”). We present theoretical results that help deal with these challenges and present tractable linear programming formulations for testing whether dominance holds between any given pair of distributions. We also propose an interactive decision support procedure for ranking a given set of distributions and demonstrate its performance through computational testing

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Inequity averse optimisation in operational research

There 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 optimisation. 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 modelling point of view, we classify three main approaches to handle equitability concerns: the fi…rst 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 briefy describe these approaches and provide a discussion of their advantages and disadvantages. We discuss future research directions focussing on decision support and robustness

Multiobjective Knapsack Problem with Equity Concerns

In this paper, a multi-objective mathematical modeling approach has been developed for resource distribution problem which has equity concerns. We assume that the preference model of the decision maker satisfies properties related to inequity-aversion, hence we focus on finding nondominated solutions in line with the properties of inequity-averse preferences, namely the equitably efficient solutions. We propose a dynamic programming (DP) based algorithm, which exploits different lower and upper bounds to eliminate partial solutions that will not lead to equitably efficient solutions. In addition to the lower bounds previously discussed in the literature, we define a new lower bound and demonstrate its effectiveness. We perform experiments to show and discuss the performances of the DP algorithm and another well-known exact approach, the epsilon constraint method, for bi-objective settings. We also provide results of the epsilon constraint method for three-objective settings

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

We consider resource allocation problems where inputs are allocated to different entities such as activities, projects or departments. In such problems a common goal is achieving a desired balance in the allocation over different categories of the entities. We propose a bi-criteria framework for trading balance off against efficiency. We define and categorise indicators based on balance distribution and propose formulations and solution algorithms which provide insight into the balance-efficiency tradeoff. 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

An exact algorithm for the minimum squared load assignment problem

In this study, we consider an assignment problem with the objective to minimize the sum of squared loads over all agents. We provide mixed integer nonlinear and linear programming formulations of the problem and present a branch and bound algorithm for their solution. The results of our computational experiment have shown the satisfactory behavior of our branch and bound algorithm.Publisher's Versio

Trading off health and financial protection benefits with multiobjective optimization

Countries which are introducing a system of Universal health coverage have to make a number of key tradeoffs, of which one is the tradeoff between the level of coverage and the degree to which patients are exposed to potentially catastrophic financial risk. In this study, we first present a way in which decision makers might be supported to focus on in a particular part of the tradeoff curve and ultimately choose an efficient solution. We then introduce some multiobjective optimization models for generating the tradeoff curves given data about potential treatment numbers, costs, and benefits. Using a dataset from Malawi, we demonstrate the approach and suggest a core index metric to make specific observations on the individual treatments. Moreover, as there has been some debate about the best way to measure financial exposure, we also investigate the extent to sensitivity of our results to the precise technical choice of financial exposure metric. Specifically, we consider two metrics, which are the total number of cases protected from catastrophic expenditure and a convex penalty function that penalizes out-of-pocket expenditures in an increasingly growing way, respectively

Exact and heuristic solution approaches for the airport gate assignment problem

© 2021 Elsevier LtdIn this study, we consider an airport gate assignment problem that assigns a set of aircraft to a set of gates. The aircraft that cannot be assigned to any gate are directed to an apron. We aim to make aircraft-gate assignments so as to minimize the number of aircraft assigned to apron and among the apron usage minimizing solutions, we aim to minimize total walking distance travelled by all passengers. The problem is formulated as a mixed-integer nonlinear programming model and then it is linearized. A branch and bound algorithm, beam search and filtered beam search algorithms that employ powerful lower and upper bounding mechanisms are developed. The results of the computational experiment have shown the satisfactory performance of the algorithms

Fair resource allocation: using welfare-based dominance constraints

In this paper we consider the problem of supporting resource allocation decisions affecting multiple beneficiaries. Such problems inherently involve efficiency-fairness trade-offs. We introduce a new approach based on the paradigm of maximizing efficiency subject to constraints to ensure that the decision is acceptably fair. In contrast to existing literature, we incorporate fairness in the form of welfare dominance, ensuring that the resultant distribution of benefits to beneficiaries is at least as good as some reference distribution with respect to a set of social welfare functions that satisfy commonly accepted efficiency and fairness related axioms. We introduce a practical means to parameterize the problem, which allows for excluding welfare functions that are deemed insufficiently or overly sensitive to inequality. This allows for analyzing the impact of changes in inequality aversion on efficiency, thus revealing the trade-off between efficiency and fairness. We develop tractable reformulations for the resulting non-linear multi-level optimization problems. We then extend this approach for cases where resources are allocated to groups of individuals with different sizes. We demonstrate the potential use of the suggested framework on two case studies: a workload allocation problem and a healthcare provisioning problem