Inequity-averse decisions in operational research

This thesis is on inequity-averse decisions in operational research, and draws on concepts from economics and operational research such as multi-criteria decision making (MCDM) and mathematical modelling. The main focus of the study is developing systematic methods and modelling to help decision makers (DMs) in situations where equity concerns are important. We draw on insights from the economics literature and base our methods on some of the widely accepted principles in this area. We discuss two equity related concerns, namely equitability and balance, which are distinguished based on whether anonymity holds or not. We review applications involving these concerns and discuss alternative ways to incorporate such concerns into operational research (OR) models. We point out some future research directions especially in using MCDM concepts in this context. Specifically, we observe that research is needed to design interactive decision support systems. Motivated by this observation, we study an MCDM approach to equitability. Our interactive approach uses holistic judgements of the DM to refine the ranking of an explicitly given (discrete) set of alternatives. The DM is assumed to have a rational preference relation with two additional equity-related axioms, namely anonymity and the Pigou-Dalton principle of transfers. We provide theoretical results that help us handle the computational difficulties due to the anonymity property. We illustrate our approach by designing an interactive ranking algorithm and provide computational results to show computational feasibility. We then consider balance concerns in resource allocation settings. Balance concerns arise when the DM wants to ensure justice over entities, the identities of which might affect the decision. We propose a bi-criteria modelling approach that has efficiency (quantified by the total output) and balance (quantified by the imbalance indicators) related criteria. We solve the models using optimization and heuristic algorithms. Our extensive computational experiments show the satisfactory behaviour of our algorithms

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 preferences. 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 another) 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 assumption 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

Bicriteria Multiresource Generalized Assignment Problem

In this study, we consider a bicriteria multiresource generalized assignment problem. Our criteria are the total assignment load and maximum assignment load over all agents. We aim to generate all nondominated objective vectors and the corresponding efficient solutions. We propose several lower and upper bounds and use them in our optimization and heuristic algorithms. The computational results have shown the satisfactory behaviors of our approaches. (c) 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 621-636, 201

The multi-resource agent bottleneck generalised assignment problem

In this study, we consider the multi resource agent bottleneck generalised assignment problem. Our aim is to minimise the maximum load over all agents. We take our motivation from an assignment problem faced in heating, ventilating and air conditioning sector. We study the linear programming (LP) relaxation of the problem. We use the optimal LP relaxation solutions in our branch and bound algorithm while defining bounding and branching schemes. We find that our branch and bound algorithm returns optimal solutions to the problems with up to 60 jobs when the number of agents is 5, and up to 30 jobs when the number of agents is 10, in less than 20 minutes. To find approximate solutions, we define a tabu search algorithm and alpha approximation algorithm. Our computational results have revealed that both algorithms can find high quality solutions to large sized instances very quickly. To the best of our knowledge our study is the first reported attempt to solve the problem. We hope our study fills an important gap in the literature

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