1st Edition
Mathematical Models for Decision Making with Multiple Perspectives An Introduction
This book brings together, in a single volume, the fields of multicriteria decision making and multiobjective optimization that are traditionally covered separately. Both fields have in common the presence of multiple perspectives of looking at and evaluating decisions to be taken but they differ in the number of available alternatives. Multicriteria approaches deal with decision processes where a finite number of alternatives have to be evaluated while, in multiobjective optimization, this number is infinite and the space of alternatives continuous. This book is written for students of applied mathematics, engineering, and economics and management, with no assumed previous knowledge on the subject, as well as for practitioners in industry looking for techniques to support decision making. The mathematical formalism is very low, so that all materials are accessible to most readers. Nonetheless, a rich bibliography allows interested readers to access more technical literature.
The textbook is organized in eleven chapters, each corresponding to a class of about two hours. A comprehensive set of examples is presented, allowing for a didactic approach when presenting the methodologies. Each chapter ends with exercises that are designed to develop problem-solving skills and to promote concepts retention.
1. Single Criterion Decision Making
2. Sequential Decisions and Introduction to Utility Theory
3. Simple Multi-Attribute Rating Technique – SMART
4. The ELECTRE Methods
5. Analytic Hierarchy Process
6. TOPSIS and Fuzzy TOPSIS
7. Multi-Objective Linear Programming
8. Lexicographic and ε-Constraint Methods
9. Weighted Sum and Distance Minimization Methods
10. Interactive Methods
11. Goal Programming
Biography
Maria Isabel Gomes is Associate Professor in the Department of Mathematics at the Faculty of Science and Technology of Nova University of Lisbon (UNL) and a researcher of the Operational Research group at the Center for Mathematics and Applications (UNL). She coordinates the master program in Mathematics and Applications at the Faculty of Science and Technology of Nova University of Lisbon. In 1996, she obtained her B.S. degree in Applied Mathematics - Operational Research at the Faculty of Science and Technology of Nova University of Lisbon. In 2001, she completed her M.S. degree in Operational Research and Systems Engineering and, in 2007, her Ph.D. in Industrial Engineering and Management at the Technical University of Lisbon. Since 1998, she is a member of the Portuguese Association of Operations Research.
Her research focuses mainly on the development of new mathematical programming models to solve real world problems in contexts such as supply chain management, logistics, transportation and routing in solid waste collection, and healthcare. She has co-authored more than 50 scientific papers and one book. In 2003, she was awarded by the EURO – Association of European Operational Research Societies - the Award for Best Paper on "Theory and Methodology" published on the European Journal of Operational Research between 2010 and 2011.
Nelson Chibeles Martins is an assistant professor at the Faculty of Science and Technology of Nova University of Lisbon and an associate researcher in the Operational Research group at the Centre for Mathematics and Applications (UNL). Storyteller and RPG Game Master since 1990. Dad since 2003.
Nelson completed his B.S. degree in Applied Mathematics - Operational Research at the Faculty of Science and Technology of the Nova University of Lisbon in 1994 and his M.S. degree in Operational Research and Systems Engineering in 1997 at the Technical University of Lisbon. Finally, in 2005, he obtained a Ph.D. in Systems Engineering also at the Technical University of Lisbon.
His main research focus is the application of metaheuristics on complex and highly combinatorial real industrial, logistic and routing problems. Additionally, he has been researching in teaching maths to young children through the use of games and hands-on activities and the impact of teaching (and learning) soft skills courses in technology and science students.
Nelson is a member of the Portuguese Association of Operations Research since 1997. He co-authored the article "Soft skills for science and technology students: A pedagogical experience" that was presented at WEEF2015 - World Engineering Education and received the Best Paper Award.
