Discrete Optimization with Interval Data: Minmax Regret and Fuzzy Approach by Ad

Description: Discrete Optimization with Interval Data by Adam Kasperski From the inception of the PERT method in the 1950s, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description Operations research often solves deterministic optimization problems based on elegantand conciserepresentationswhereall parametersarepreciselyknown. In the face of uncertainty, probability theory is the traditional tool to be appealed for, and stochastic optimization is actually a signi?cant sub-area in operations research. However, the systematic use of prescribed probability distributions so as to cope with imperfect data is partially unsatisfactory. First, going from a deterministic to a stochastic formulation, a problem may becomeintractable. Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling problems like PERT. From the inception of the PERT method in the 1950s, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. Even if the power of todays computers enables the stochastic PERT to be addressed to a large extent, still its solutions often require simplifying assumptions of some kind. Another di?culty is that stochastic optimization problems produce solutions in the average. For instance, the criterion to be maximized is more often than not expected utility. This is not always a meaningful strategy. In the case when the underlying process is not repeated a lot of times, let alone being one-shot, it is not clear if this criterion is realistic, in particular if probability distributions are subjective. Expected utility was proposed as a rational criterion from ?rst principles by Savage. In his view, the subjective probability distribution was - sically an artefact useful to implement a certain ordering of solutions. Notes Novel research results in the field of Discrete Optimization with Interval DataPresents a new approach (robust optimization) to modeling incomplete knowledge Back Cover 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. Author Biography 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 import Table of Contents Minmax Regret Combinatorial Optimization Problems with Interval Data.- Problem Formulation.- Evaluation of Optimality of Solutions and Elements.- Exact Algorithms.- Approximation Algorithms.- Minmax Regret Minimum Selecting Items.- Minmax Regret Minimum Spanning Tree.- Minmax Regret Shortest Path.- Minmax Regret Minimum Assignment.- Minmax Regret Minimum s???t Cut.- Fuzzy Combinatorial Optimization Problem.- Conclusions and Open Problems.- Minmax Regret Sequencing Problems with Interval Data.- Problem Formulation.- Sequencing Problem with Maximum Lateness Criterion.- Sequencing Problem with Weighted Number of Late Jobs.- Sequencing Problem with the Total Flow Time Criterion.- Conclusions and Open Problems.- Discrete Scenario Representation of Uncertainty. Long Description Operations research often solves deterministic optimization problems based on elegantand conciserepresentationswhereall parametersarepreciselyknown. In the face of uncertainty, probability theory is the traditional tool to be appealed for, and stochastic optimization is actually a signicant sub-area in operations research. However, the systematic use of prescribed probability distributions so as to cope with imperfect data is partially unsatisfactory. First, going from a deterministic to a stochastic formulation, a problem may becomeintractable. Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling problems like PERT. From the inception of the PERT method in the 1950s, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. Even if the power of todays computers enables the stochastic PERT to be addressed to a large extent, still its solutions often require simplifying assumptions of some kind. Another diculty is that stochastic optimization problems produce solutions in the average. For instance, the criterion to be maximized is more often than not expected utility. This is not always a meaningful strategy. In the case when the underlying process is not repeated a lot of times, let alone being one-shot, it is not clear if this criterion is realistic, in particular if probability distributions are subjective. Expected utility was proposed as a rational criterion from ?rst principles by Savage. In his view, the subjective probability distribution was - sically an artefact useful to implement a certain ordering of solutions. Feature Novel research results in the field of Discrete Optimization with Interval Data Presents a new approach (robust optimization) to modeling incomplete knowledge Details ISBN3642097200 Author Adam Kasperski Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Series Studies in Fuzziness and Soft Computing Year 2010 ISBN-10 3642097200 ISBN-13 9783642097201 Format Paperback Publication Date 2010-11-23 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 620 Edition 1st Short Title DISCRETE OPTIMIZATION W/INTERV Language English Media Book Series Number 228 Subtitle Minmax Regret and Fuzzy Approach Pages 220 DOI 10.1007/978-3-540-78484-5 Edition Description Softcover reprint of hardcover 1st ed. 2008 Alternative 9783540784838 Illustrations XVI, 220 p. Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:144333827;

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