The Structure of Fair Solutions

This book provides a novel and unifying perspective on the structural properties of fair solutions in optimization formulations. The book also addresses a growing interest in incorporating fairness into the models that lie behind many business and public policy decisions. Since there are several ways to formulate fairness mathematically, the authors characterize optimal solutions that result from different formulations with the aim of informing the choice of an appropriate model for a given application. The focus is on fairness criteria that combine efficiency with fairness since typically both are important in practice. Most of these results are new and do not appear in the current literature. The book is directed towards a wide range of audiences including practitioners, researchers in mathematical optimization, and welfare economists.

In addition, this book:

• Presents practical linear, nonlinear, or mixed integer programming formulations and a wide variety of fairness models
• Includes detailed proofs that provide insight into the properties of each criterion
• Provides guidelines for selecting a fairness model and the tendency to incentivize cooperation or competition
  About the Authors

Özgün Elçi, Ph.D., is a Research Scientist on the Modeling and Optimization team at Amazon.

John Hooker, Ph.D. is University Professor of Operations Research and T. Jerome Holleran Professor of Business Ethics and Social Responsibility, Emeritus, at Carnegie Mellon University.

Peter Zhang, Ph.D, is an Assistant Professor at Carnegie Mellon University's Heinz College of Information Systems and Public Policy.

Presents practical linear, nonlinear, or mixed integer programming formulations and a wide variety of fairness models Includes detailed proofs that provide insight into the properties of each criterion Provides guidelines for selecting a fairness model and the tendency to incentivize cooperation or competition

Autorentext

Özgün Elçi, Ph.D., is a Research Scientist on the Modeling and Optimization team at Amazon. He has a Ph.D. in Operations Research from Tepper School of Business at Carnegie Mellon University. During his doctoral studies, he worked on applying logic-based Benders decomposition to stochastic scheduling problems. He also worked on robust portfolio optimization and fair allocation of resources. Prior to that, he focused on humanitarian relief network design problems under uncertainty. His current research interests include solving large-scale network design problems that arise in industry via decomposition-based exact methods. 

John Hooker, Ph.D. is University Professor of Operations Research and T. Jerome Holleran Professor of Business Ethics and Social Responsibility, Emeritus, at Carnegie Mellon University. He holds doctoral degrees in philosophy and operations research.  He has published 200+ articles, 10 books, and six edited volumes in operations research, constraint programming, ethics, the mathematical analysis of fairness, cross-cultural management, and music theory. He is a Fellow of the Institute for Operations Research and the Management Sciences (INFORMS), as well as recipient the INFORMS Computing Society Prize, the INFORMS Khachiyan Award for lifetime achievements in optimization, the Research Excellence Award of the Association for Constraint Programming, and several best paper awards.  He is a pioneer in the integration of optimization and constraint programming technologies, now a feature of leading optimization solvers.  He developed a substantial generalization of Benders decomposition that has seen hundreds of practical applications.  In addition, he and Tarik Hadi introduced an approach to optimization based on decision diagrams.   Presently, his main research area is the mathematical analysis of fairness.  His ethics-related books include Business Ethics as Rational Choice, Working across Cultures, Taking Ethics Seriously, Advanced Introduction to Business Ethics, and Toward Systematic Normative Ethics (forthcoming). He served as founding editor-in-chief of the Journal of Business Ethics Education, the only academic journal dedicated to the topic.

Peter Zhang, Ph.D, is an Assistant Professor at Carnegie Mellon University’s Heinz College of Information Systems and Public Policy. His research interests include robust and stochastic optimization theory, with applications in supply chain and transportation. He obtained Ph.D. from MIT in Engineering Systems and BASc and MASc from the University of Toronto. His Ph.D. thesis contributed to the identification of vulnerabilities in supply chain networks and robust supply chain network design methods. Some concepts that Peter worked on and developed at MIT (time-to-recover, supply chain stress test, and robust supply chains) have been cited in various media outlets, academic journals, and White House reports. He has received multiple paper competition awards in academic and applied research areas at INFORMS and POM conferences.

Inhalt

Chapter 1. Introduction.- A Generic Optimization Model with Fairness.- Chapter 2. Hierarchical Distribution.- Chapter 3. Incentives and Sharing.- Chapter 4. Axiomatic and Bargaining Arguments.- Inequality Metrics.- Chapter 5. Maximin and Leximax Criteria.- Chapter 6. Beta Fairness.- Chspter 7. Alpha Fairness and the Nash Bargaining Solution.- Chapter 8.The Kalai-Smorodinsky Bargaining Solution.- Chapter 9. Utility Threshold Criteria.- Chapter 10. Equity Threshold Criteria.- Chapter 11. Utility Threshold Criteria with Leximax.- Chapter 12. Summary of Results.