In operations research applications we are often faced with the problem of incomplete or uncertain data. This book considers solving combinatorial optimization problems with imprecise data modeled by intervals and fuzzy intervals. It focuses on some basic and traditional problems, such as minimum spanning tree, shortest path, minimum assignment, minimum cut and various sequencing problems. The interval based approach has become very popular in the recent decade. Decision makers are often interested in hedging against the risk of poor (worst case) system performance. This is particularly important for decisions that are encountered only once. In order to compute a solution that behaves reasonably under any likely input data, the maximal regret criterion is widely used. Under this criterion we seek a solution that minimizes the largest deviation from optimum over all possible realizations of the input data.
The minmax regret approach to discrete optimization with interval data has attracted considerable attention in the recent decade. This book summarizes the state of the art in the area and addresses some open problems. Furthermore, it contains a chapter devoted to the extension of the framework to the case when fuzzy intervals are applied to model uncertain data. The fuzzy intervals allow a more sophisticated uncertainty evaluation in the setting of possibility theory.
This book is a valuable source of information for all operations research practitioners who are interested in modern approaches to problem solving. Apart from the description of the theoretical framework, it also presents some algorithms that can be applied to solve problems that arise in practice.