Combinatorial Optimization Under Uncertainty: Real-Life Scenarios in Allocation Problems

This book discusses the basic ideas, underlying principles, mathematical formulations, analysis and applications of the different combinatorial problems under uncertainty and attempts to provide solutions for the same. Uncertainty influences the behaviour of the market to a great extent. Global pandemics and calamities are other factors which affect and augment unpredictability in the market. The intent of this book is to develop mathematical structures for different aspects of allocation problems depicting real life scenarios. The novel methods which are incorporated in practical scenarios under uncertain circumstances include the STAR heuristic approach, Matrix geometric method, Ranking function and Pythagorean fuzzy numbers, to name a few. Distinct problems which are considered in this book under uncertainty include scheduling, cyclic bottleneck assignment problem, bilevel transportation problem, multi-index transportation problem, retrial queuing, uncertain matrix games, optimal production evaluation of cotton in different soil and water conditions, the healthcare sector, intuitionistic fuzzy quadratic programming problem, and multi-objective optimization problem. This book may serve as a valuable reference for researchers working in the domain of optimization for solving combinatorial problems under uncertainty. The contributions of this book may further help to explore new avenues leading toward multidisciplinary research discussions.

Dr. Ritu Arora received her Ph.D degree from University of Delhi, India. She has a teaching experience of 20 years in University of Delhi. Her research specialization is in the field of mathematical programming and its application to allocation problems. She is currently working as a Professor in the Department of Mathematics, Keshav Mahavidyalaya, University of Delhi.

Prof. Shalini Arora is presently working as Professor in Mathematics at Applied Sciences and Humanities Department, IGDTUW. She has more than 20 years of Teaching experience. She did her Masters and Ph.D in Mathematics from IIT Delhi. She is a recipient of the ’Young Scientist Award’ by the SERC division of DST. She has a teaching experience of more than 19 years. Her areas of research interest include Mathematical Programming, Allocation Problems viz., Transportation and Assignment Problems, Combinatorial optimization etc.

Dr. Anand J Kulkarni holds a PhD in Distributed Optimization from Nanyang Technological University, Singapore. He worked as Research Fellow at Odette School of Business, University of Windsor, Canada. He is currently working as Professor and Associate Director of the Institute of AI at the MITWPU, Pune, India.

Dr. Patrick Siarry received a PhD degree from the University Paris 6, in 1986 and the Doctorate of Sciences (Habilitation) from the University Paris 11, in 1994. Since 1995, he is working as a professor in automatics and informatics. His main research interests are design of new stochastic global optimization heuristics and their applications to various engineering fields.