Risk-averse stochastic programming provides means to incorporate a wide range of risk attitudes into decision making. Pioneered by the advances in financial optimization, several risk measures such as Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) are employed in risk-averse stochastic programming for a variety of application areas. In this work, we consider risk-averse modeling approaches for stochastic multicriteria and stochastic sequential decision-making problems. First, we propose a new multivariate definition for CVaR as a set of vectors. We analyze its properties and establish that the new definition remedies some potential drawbacks of the existing definitions for discrete random variables. Motivated by the computational challenges in the optimization of vector-valued multivariate definitions of CVaR, next, we study two-stage stochastic programming problems with multivariate risk constraints utilizing a scalarization scheme. We formulate this problem as a mixed-integer program (MIP) and devise two delayed cut generation algorithms. The effectiveness of the proposed modeling approach and solution methods are demonstrated on a pre-disaster relief network design problem. Finally, we study the Markov Decision Processes (MDPs) under cost and transition probability uncertainty with the objective of optimizing the VaR associated with the expected performance of an MDP model. Based on a sampling approach, we provide an MIP formulation and a branch-and-cut algorithm, and demonstrate our proposed methods on an inventory management problem for long-term humanitarian relief operations.

Multiple Criteria Decision Making and its Applications to Economic Problems ties Multiple Criteria Decision Making (MCDM)/Multiple Objective Optimization (MO) and economics together. It describes how MCDM methods (goal programming) can be used in economics. The volume consists of two parts. Part One of the book introduces the MCDM approaches. This first part, comprising Chapters 1-5, is basically an overview of MCDM methods that can most likely be used to address a wide range of economic problems. Readers looking for an in-depth discussion of multi-criteria analysis can grasp and become acquainted with the initial MCDM tools, language and definitions. Part Two, which comprises Chapters 6-8, focuses on the theoretical core of the book. Thus in Chapter 6 an economic meaning is given to several key concepts on MCDM, such as ideal point, distance function, etc. It illustrates how Compromise Programming (CP) can support the standard premise of utility optimisation in economics as well as how it is capable of approximating the standard utility optimum when the decision-makers' preferences are incompletely specified. Chapter 7 deals entirely with production analysis. The main characteristic throughout the Chapter refers to a standard joint production scenario, analysed from the point of view of MCDM schemes. Chapter 8 focuses on the utility specification problem in the n-arguments space within a risk aversion context. A link between Arrows' risk aversion coefficient and CP utility permits this task. The book is intended for postgraduate students and researchers in economics with an OR/MS orientation or in OR/MS with an economic orientation. In short, it attempts to fruitfully link economics and MCDM.

This monograph presents new developments in multi-level decision-making theory, technique and method in both modeling and solution issues. It especially presents how a decision support system can support managers in reaching a solution to a multi-level decision problem in practice. This monograph combines decision theories, methods, algorithms and applications effectively. It discusses in detail the models and solution algorithms of each issue of bi-level and tri-level decision-making, such as multi-leaders, multi-followers, multi-objectives, rule-set-based, and fuzzy parameters. Potential readers include organizational managers and practicing professionals, who can use the methods and software provided to solve their real decision problems; PhD students and researchers in the areas of bi-level and multi-level decision-making and decision support systems; students at an advanced undergraduate, master’s level in information systems, business administration, or the application of computer science.

This book considers a broad range of areas from decision making methods applied in the contexts of Risk, Reliability and Maintenance (RRM). Intended primarily as an update of the 2015 book Multicriteria and Multiobjective Models for Risk, Reliability and Maintenance Decision Analysis, this edited work provides an integration of applied probability and decision making. Within applied probability, it primarily includes decision analysis and reliability theory, amongst other topics closely related to risk analysis and maintenance. In decision making, it includes multicriteria decision making/aiding (MCDM/A) methods and optimization models. Within MCDM, in addition to decision analysis, some of the topics related to mathematical programming areas are considered, such as multiobjective linear programming, multiobjective nonlinear programming, game theory and negotiations, and multiobjective optimization. Methods related to these topics have been applied to the context of RRM. In MCDA, several other methods are considered, such as outranking methods, rough sets and constructive approaches. The book addresses an innovative treatment of decision making in RRM, improving the integration of fundamental concepts from both areas of RRM and decision making. This is accomplished by presenting current research developments in decision making on RRM. Some pitfalls of decision models on practical applications on RRM are discussed and new approaches for overcoming those drawbacks are presented.

This book integrates multiple criteria concepts and methods for problems within the Risk, Reliability and Maintenance (RRM) context. The concepts and foundations related to RRM are considered for this integration with multicriteria approaches. In the book, a general framework for building decision models is presented and this is illustrated in various chapters by discussing many different decision models related to the RRM context. The scope of the book is related to ways of how to integrate Applied Probability and Decision Making. In Applied Probability, this mainly includes: decision analysis and reliability theory, amongst other topics closely related to risk analysis and maintenance. In Decision Making, it includes a broad range of topics in MCDM (Multi-Criteria Decision Making) and MCDA (Multi-Criteria Decision Aiding; also known as Multi-Criteria Decision Analysis). In addition to decision analysis, some of the topics related to Mathematical Programming area are briefly considered, such as multiobjective optimization, since methods related to these topics have been applied to the context of RRM. The book addresses an innovative treatment for the decision making in RRM, thereby improving the integration of fundamental concepts from the areas of both RRM and decision making. This is accomplished by presenting an overview of the literature on decision making in RRM. Some pitfalls of decision models when applying them to RRM in practice are discussed and guidance on overcoming these drawbacks is offered. The procedure enables multicriteria models to be built for the RRM context, including guidance on choosing an appropriate multicriteria method for a particular problem faced in the RRM context. The book also includes many research advances in these topics. Most of the multicriteria decision models that are described are specific applications that have been influenced by this research and the advances in this field. Multicriteria and Multiobjective Models for Risk, Reliability and Maintenance Decision Analysis is implicitly structured in three parts, with 12 chapters. The first part deals with MCDM/A concepts methods and decision processes. The second part presents the main concepts and foundations of RRM. Finally the third part deals with specific decision problems in the RRM context approached with MCDM/A models.

This book provides a broad coverage of the recent advances in robustness analysis in decision aiding, optimization, and analytics. It offers a comprehensive illustration of the challenges that robustness raises in different operations research and management science (OR/MS) contexts and the methodologies proposed from multiple perspectives. Aside from covering recent methodological developments, this volume also features applications of robust techniques in engineering and management, thus illustrating the robustness issues raised in real-world problems and their resolution within advances in OR/MS methodologies. Robustness analysis seeks to address issues by promoting solutions, which are acceptable under a wide set of hypotheses, assumptions and estimates. In OR/MS, robustness has been mostly viewed in the context of optimization under uncertainty. Several scholars, however, have emphasized the multiple facets of robustness analysis in a broader OR/MS perspective that goes beyond the traditional framework, seeking to cover the decision support nature of OR/MS methodologies as well. As new challenges emerge in a “big-data'” era, where the information volume, speed of flow, and complexity increase rapidly, and analytics play a fundamental role for strategic and operational decision-making at a global level, robustness issues such as the ones covered in this book become more relevant than ever for providing sound decision support through more powerful analytic tools.