Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction.

This collection of formulas constitutes a compendium of mathematics for eco­ nomics and business. It contains the most important formulas, statements and algorithms in this significant subfield of modern mathematics and addresses primarily students of economics or business at universities, colleges and trade schools. But people dealing with practical or applied problems will also find this collection to be an efiicient and easy-to-use work of reference. First the book treats mathematical symbols and constants, sets and state­ ments, number systems and their arithmetic as well as fundamentals of com­ binatorics. The chapter on sequences and series is followed by mathematics of finance, the representation of functions of one and several independent vari­ ables, their differential and integral calculus and by differential and difference equations. In each case special emphasis is placed on applications and models in economics. The chapter on linear algebra deals with matrices, vectors, determinants and systems of linear equations. This is followed by the representation of struc­ tures and algorithms of linear programming. Finally, the reader finds formu­ las on descriptive statistics (data analysis, ratios, inventory and time series analysis), on probability theory (events, probabilities, random variables and distributions) and on inductive statistics (point and interval estimates, tests). Some important tables complete the work.

The book presents applications of stochastic calculus to derivative security pricing and interest rate modelling. By focusing more on the financial intuition of the applications rather than the mathematical formalities, the book provides the essential knowledge and understanding of fundamental concepts of stochastic finance, and how to implement them to develop pricing models for derivatives as well as to model spot and forward interest rates. Furthermore an extensive overview of the associated literature is presented and its relevance and applicability are discussed. Most of the key concepts are covered including Ito’s Lemma, martingales, Girsanov’s theorem, Brownian motion, jump processes, stochastic volatility, American feature and binomial trees. The book is beneficial to higher-degree research students, academics and practitioners as it provides the elementary theoretical tools to apply the techniques of stochastic finance in research or industrial problems in the field.

People are facing more and more NP-complete or NP-hard problems of a combinatorial nature and of a continuous nature in economic, military and management practice. There are two ways in which one can enhance the efficiency of searching for the solutions of these problems. The first is to improve the speed and memory capacity of hardware. We all have witnessed the computer industry's amazing achievements with hardware and software developments over the last twenty years. On one hand many computers, bought only a few years ago, are being sent to elementary schools for children to learn the ABC's of computing. On the other hand, with economic, scientific and military developments, it seems that the increase of intricacy and the size of newly arising problems have no end. We all realize then that the second way, to design good algorithms, will definitely compensate for the hardware limitations in the case of complicated problems. It is the collective and parallel computation property of artificial neural net­ works that has activated the enthusiasm of researchers in the field of computer science and applied mathematics. It is hard to say that artificial neural networks are solvers of the above-mentioned dilemma, but at least they throw some new light on the difficulties we face. We not only anticipate that there will be neural computers with intelligence but we also believe that the research results of artificial neural networks might lead to new algorithms on von Neumann's computers.

This monograph is the proceedings of a symposium held at the University of California at Berkeley, September 12-14, 1990. It was sponsored by the Electric Power Research Institute (EPR!) and by the University of California University-Wide Energy Research Group (UERG). The sympo­ sium brought together researchers and practitioners from academia, the utility industry, private and public organizations and regulatory agencies to address various challenges and opportunities related to product differen­ tiation in the electric power industry. Electric utilities are evolving rapidly from commodity-oriented services to product-oriented services. Utilities are offering menus of service options tailored to the needs of different customers. Reliability is one important dimension of electric service that lends itself to such product differentia­ tion., Options include lower rate curtail able services for industrial cus­ tomers, higher reliability power for some commercial customers, and load control with rebates for residential customers., These specialized services are a first step toward the product differentiation goal of allowing all customers to choose the type of service best suited to their electricity needs. The symposium provided a forum for in depth examination of the complex planning, development, and implementation issues associated with differ­ entiated products. Its specific objectives were to: xviii • Review the state of the art in implementing reliability differ­ entiated electric services. • Address the entire process for developing and implementing reliability differentiated product menus including research, design, marketing, implementation, and evaluation. • Consider technical, economic, and regulatory barriers to imple­ menting reliabilitydifferentiated product design.

This book delves deeply into the research progress on three-way risk decision for risk management under complex social environment. From the new perspective of collective wisdom, it systematically explores three-way group decision-making methods and practical applications by considering group information fusion, consensus reaching process, group social network and group complex network. This book intends to provide a reference for researchers, practitioners and graduate students in the fields of risk management and decision analysis.

I have been pleased with the favourable reception of the first edition of this book and I am grateful to have the opportunity to prepare this second edition. In this revised and enlarged edition I corrected some misprints and errors that occurred in the first edition (fortunately I didn't find too many) and I added a large number of notes that give the reader an impression of what kind of results have been obtained since the first edition was printed and that give an indication of the direction the subject is taking. Many of the notes discuss (or refer to papers discussing) applications of the refinements that are considered. Of course, it is the quantity and the quality of the insights and the applications that lend the refinements their validity. Although the guide to the applications is far from complete, the notes certainly allow the reader to form a good judgement of which refinements have really yielded new insights. Hence, as in the first edition, I will refrain from speculating on which refinements of Nash equilibria will survive in the long run. To defend this position let me also cite Binmore [1990] who compares writing about refinements to the Herculean task of defeating the nine-headed Hydra which grew too heads for each that was struck off. It is a pleasure to have the opportunity to thank my secretary, Marjoleine de Wit, who skilfully and, as always, cheerfully typed the manuscript and did the proofreading.

The vehicle routing problem (VRP) is one of the most famous combinatorial optimization problems. In simple terms, the goal is to determine a set of routes with overall minimum cost that can satisfy several geographical scattered - mands. A ?eet of vehicles located in one or more depots is available to ful?ll the requests. A large number of variants exist, adding di?erent constraints to the original de?nition. Some examples are related to the number of depots, the ordering for visiting the customers or to time windows specifying a desirable period to arrive to a given location. The original version of this problem was proposed by Dantzig and Ramser in 1959 [1]. In their seminal paper, the authors address the calculation of a set of optimal routes for a ?eet of gasoline delivery trucks. Since then, the VRP has attractedtheattentionofalargenumberofresearchers.Aconsiderablepartofits success is a consequence of its practical interest, as it resembles many real-world problems faced everyday by distribution and transportation companies, just to mention a few applications areas. In this context, the development of e?cient optimization techniques is crucial. They are able to provide new and enhanced solutionstologisticoperations,andmaythereforeleadtoasubstantialreduction in costs for companies. Additionally, and from a research oriented perspective, the VRP is a challenging NP-hard problem providing excellent benchmarks to access the e?ciency of new global optimization algorithms.

1 DATA ENVELOPMENT ANALYSIS Data Envelopment Analysis (DEA) was initially developed as a method for assessing the comparative efficiencies of organisational units such as the branches of a bank, schools, hospital departments or restaurants. The key in each case is that they perform feature which makes the units comparable the same function in terms of the kinds of resource they use and the types of output they produce. For example all bank branches to be compared would typically use staff and capital assets to effect income generating activities such as advancing loans, selling financial products and carrying out banking transactions on behalf of their clients. The efficiencies assessed in this context by DEA are intended to reflect the scope for resource conservation at the unit being assessed without detriment to its outputs, or alternatively, the scope for output augmentation without additional resources. The efficiencies assessed are comparative or relative because they reflect scope for resource conservation or output augmentation at one unit relative to other comparable benchmark units rather than in some absolute sense. We resort to relative rather than absolute efficiencies because in most practical contexts we lack sufficient information to derive the superior measures of absolute efficiency. DEA was initiated by Charnes Cooper and Rhodes in 1978 in their seminal paper Chames et al. (1978). The paper operationalised and extended by means of linear programming production economics concepts of empirical efficiency put forth some twenty years earlier by Farrell (1957).

This book presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book concludes with a problem section. Hints, answers and solutions are included.

Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

Understanding the stochastic enviornment is as much important to the manager as to the economist. From production and marketing to financial management, a manager has to assess various costs imposed by uncertainty. The economist analyzes the role of incomplete and too often imperfect information structures on the optimal decisions made by a firm. The need for understanding the role of uncertainty in quantitative decision models, both in economics and management science provide the basic motivation of this monograph. The stochastic environment is analyzed here in terms of the following specific models of optimization: linear and quadratic models, linear programming, control theory and dynamic programming. Uncertainty is introduced here through the para­ meters, the constraints, and the objective function and its impact evaluated. Specifically recent developments in applied research are emphasized, so that they can help the decision-maker arrive at a solution which has some desirable charac­ teristics like robustness, stability and cautiousness. Mathematical treatment is kept at a fairly elementary level and applied as­ pects are emphasized much more than theory. Moreover, an attempt is made to in­ corporate the economic theory of uncertainty into the stochastic theory of opera­ tions research. Methods of optimal decision rules illustrated he re are applicable in three broad areas: (a) applied economic models in resource allocation and economic planning, (b) operations research models involving portfolio analysis and stochastic linear programming and © systems science models in stochastic control and adaptive behavior.

This book integrates for readers three areas of knowledge, pertaining to risk-based project decision making: project risk management (PRM), complexity theory, and decision-making under deep uncertainty (DMDU). Readers will appreciate that in practice, too often relevant complexity and uncertainty factors are either ignored or overlooked resulting in epic project failures. The author discusses a variety of methodologies and a decision-tree-type framework to determine why, when and how particular methodologies should be applied to ensure project success. These include nonlinear Monte Carlo techniques, a dynamic adaptive methodology to adapt to external environment changes, game theory for devising robust decision-making criteria, systems dynamics and cost escalation modelling, as well as risk-based & economic-based alternatives selection methodologies. This book will be an eye-opener for many PRM practitioners, helping to increase their chances of project success by properly handling inescapable project-complexity and deep-uncertainty implications in specific contexts.

This book lays out a foundation and taxonomy for Behavioral Decision Analysis, featuring representative work across various domains. Traditional research in the domain of Decision Analysis has focused on the design and application of logically consistent tools to support decision makers during the process of structuring problem complexity, modeling uncertainty, generating predictions, eliciting preferences, and, ultimately, making better decisions. Two commonly held assumptions are that the decision maker’s cognitive belief system is fully accessible and that this system can be understood and formalized by trained analysts. However, in past years, an active line of research has emerged studying instances in which such assumptions may not hold. This book unites this community under the common theme of Behavioral Decision Analysis. The taxonomy used in this book categorizes research based on task focus (prediction or decision) and behavioral level (individual or group). Two theoretical lenses that lie at the interface between (1) normative and descriptive research, and (2) normative and prescriptive research are introduced. The book then proceeds to highlight representative works across the two lenses focused on individual and group-level decision making. Featuring various methodologies and applications, the book serves as a reference for researchers, students, and professionals across different disciplines with a common interest in Behavioral Decision Analysis.

This volume uses advanced machine learning techniques to analyze government communication to evaluate policy effectiveness. The book develops policy effectiveness foundation models by cohorting historical budget policies with statistical models which are built on well reputed data sources including economic events, macroeconomic trends, and ratings and commerce terms from international institutions. By signal mining policies to the economic outcome patterns, the book aims to create a rich source of successful policy insights in terms of their effectiveness in bringing development to the poor and underserved communities to ensure the spread of wealth, social wellbeing, and standard of living to the common denomination of society rather than a selected quotient. Enabling academics and practitioners across disciplines to develop applications for effective policy interventions, this volume will be of interest to a wide audience including software engineers, data scientists, social scientists, economists, and agriculture practitioners.