Network Optimization: An Introduction to the Network Reconstruction Approach

For every problem, mathematical or otherwise, there is more than one approach and much depends on the ingenuity of the person concerned. Consider that a person is interested in picking some fruit from a tree and is considering multiple picking options. One possibility is, if one can reach the fruit, just snip it to retrieve it. The second possibility is to alternatively apply force and detach the fruit from the tree. If neither option is possible, the fruit can still be detached from the tree, but how? A third possibility lies in the fact that just holding on to the fruit and turning it in one direction it can be picked. Similarly, many possibilities are seen by keen eyes while solving a mathematical problem. The reconstruction approach applied in this book is like the third possibility of holding a fruit and turning it in one direction until the desired solution is obtained.

This book is an introduction to reconstruction concepts and their applications for solving some network optimization problems. Networks are a mathematical abstraction of a given physical situation, which are described by using nodes, links (directed or non-directed) and link weights defining some associated properties of that physical system. Reconstruction ideas exploit the mathematical structure of a particular problem and find ways to reach the required solution. It is hoped that these ideas will be explored for other mathematical structures.

The authors have developed many methods to find optimal solutions for these network related problems and they observed that various methods discussed in 8 chapters have a common thread of reconstruction, which unites them, and that aspect motivated authors to develop this book.

Elias Munapo holds a B.Sc. (Hons) in Applied Mathematics (1997), M.Sc. in Operations Research (2002) and a Ph.D. in Operations Research (2010), all from the National University of Science and Technology (NUST), Zimbabwe. He also has a certificate in outcomes-based assessment in Higher Education and Open Distance Learning, University of South Africa (UNISA) and a certificate in University Education Induction Program, University of KwaZulu-Natal (UKZN). He is a Professional Natural Scientist certified by the South African Council for Natural Scientific Professions (SACNASP), 2012; and NRF rated in South Africa. He has published/co-published over 120 articles and two books. He has also edited/co-edited 7 books and is a guest editor of Applied Sciences, Algorithms and Next Energy journals which are under MDPI. He has supervised/co-supervised eleven doctoral students and over 30 students at Master level. He is a member of the Operations Research Society of South Africa, Executive Committee Member 2012-13, South African Council for Natural Scientific Professions (SACNASP) as a Certified Natural Scientist, European Conference on Operational Research (EURO) and the International Federation of Operations Research Societies (IFORS), a member of the International Conference on Optimization (ICO) and is part of the team preparing to host ICO 2026 at Johannesburg.

Santosh Kumar OAM received his Ph.D. degree in Operations Research from Delhi University. He is author and co-author of over 210 papers and 4 books in the field of operations research. His contributions in the field of OR have been recognized in the form of the 'Ren Pots' award from the Australian Society for operations Research (ASOR) in 2009 and a recognition award from the South African OR Society as a non-member of the society and a non-resident of South Africa in 2011. He was the President of the Asia Pacific Operations Research societies (1995-97), where ASOR was a member along with 7 other countries in the region. He is currently an Honorary Professor at RMIT University, Melbourne. He is a Fellow of the Institute of Mathematics and its Applications, UK. On 14 June 2021, he was awarded a medal of the Order of Australia (OAM).

Philimon Nyamugure gained a B.Sc. (Hons) in 1998, an M.Sc. in 2002 and a Post Graduate Diploma in Higher Education in 2013, all from NUST, and a Ph.D. in Statistics, University of Limpopo, 2017. He joined NUST in 2003 and was Chairperson for the Departments of Applied Mathematics (2009-2013) and Chairman, Department of Statistics and Operations Research (2013-2019). He became Executive Dean of the Faculty of Applied Science from 2020 to date and a University Senator from 2009 and Councillor from 2020 to date. He received an award for the best Ph.D. presenter in the School of Mathematical and Computer Sciences, University of Limpopo. Best Senior presenter, Faculty of Applied Sciences, and in 2017 was awarded a Fulbright Research Award for African Scholars. He is involved in several community engagement programs including National University of Science and Technology Schools Enrichment Program (NUSTSEP). He is currently an Executive Dean and a Professor at NUST.

Trust Tawanda is a seasoned academic and researcher with a strong background in Operations Research and Statistics. He holds a Bachelor of Science (Hons) in Operations Research and Statistics (2013), a Master of Science in Operations Research and Statistics (2017), and a Ph.D. in Operations Research (2024) from the National University of Science and Technology (NUST) in Zimbabwe. Currently, he is pursuing a Post Graduate Diploma in Higher and Tertiary Education (PGDHTE) at Great Zimbabwe University (GZU). As a Lecturer in the Department of Statistics and Operations Research at NUST's Faculty of Applied Sciences, he teaches and conducts research in his areas of expertise, which include network optimization problems, transportation problems, travelling salesman problems, and assignment problems. He has a notable publication record, with papers and book chapters to his credit. His academic journey and research endeavors demonstrate his commitment to advancing knowledge in operations research.