The thesis focuses on the analysis of various extensions of the classical multi-period single-item stochastic inventory problem. Specifically, we investigate two particular approaches of modeling risk in the context of inventory management: risk-averse models and robust formulations. We analyze the classical newsvendor problem utilizing a coherent risk measure as the objective function. Properties of coherent risk measures allow us to offer a unifying treatment of risk averse and min-max type formulations. We show that the structure of the optimal policy of the risk-averse model is similar to that of the classical expected value problem for both single and multi-period cases. The result carries over even when there is a fixed ordering cost. We expand our analysis to robust formulations of multi-period inventory problems. We consider both independent and dependent uncertainty sets and prove the optimality of base-stock policies for the general problem formulation. We focus on budget of uncertainty approach and develop a heuristic that can also be employed for a class of parametric dependency structures. We compare our proposed heuristic against alternative solution techniques.
This book is dedicated to Jinhua Cao on the occasion of his 80th birthday. Jinhua Cao is one of the most famous reliability theorists. His main contributions include: published over 100 influential scientific papers; published an interesting reliability book in Chinese in 1986, which has greatly influenced the reliability of education, academic research and engineering applications in China; initiated and organized Reliability Professional Society of China (the first part of Operations Research Society of China) since 1981. The high admiration that Professor Cao enjoys in the reliability community all over the world was witnessed by the enthusiastic response of each contributor in this book. The contributors are leading researchers with diverse research perspectives. The research areas of the book iclude a broad range of topics related to reliability models, queueing theory, manufacturing systems, supply chain finance, risk management, Markov decision processes, blockchain and so forth. The book consists of a brief Preface describing the main achievements of Professor Cao; followed by congratulations from Professors Way Kuo and Wei Wayne Li, and by Operations Research Society of China, and Reliability Professional Society of China; and further followed by 25 articles roughly grouped together. Most of the articles are written in a style understandable to a wide audience. This book is useful to anyone interested in recent developments in reliability, network security, system safety, and their stochastic modeling and analysis.
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.
Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. In Lectures on Stochastic Programming: Modeling and Theory, Second Edition, the authors introduce new material to reflect recent developments in stochastic programming, including: an analytical description of the tangent and normal cones of chance constrained sets; analysis of optimality conditions applied to nonconvex problems; a discussion of the stochastic dual dynamic programming method; an extended discussion of law invariant coherent risk measures and their Kusuoka representations; and in-depth analysis of dynamic risk measures and concepts of time consistency, including several new results.
This book presents the XXII Congress of APDIO – IO 2022 which is the 22nd edition of the regular meeting of the Portuguese Association of Operational Research (APDIO). The APDIO regular meetings aim to gather Portuguese and international researchers, scholars and practitioners, as well as M.Sc. and Ph.D. students, working in the field of Operations Research to present and discuss their latest research works. The main theme of the XXII Congress of APDIO is OR in Turbulent Times: Adaptation and Resilience. Readers find interesting results and applications of Operational Research cutting-edge methods and techniques in the wide variety of the addressed problems. Of particular interest are the applications of, among others, linear, nonlinear and mixed-integer programing, multiobjective optimization, metaheuristics and hybrid heuristics, multicriteria decision analysis, data envelopment analysis, simulation, clustering techniques and decision support systems, in different areas such as, supply chain management, scheduling problems, production management, logistics, energy, telecommunications, finance and health.
Traditional supply chain management models typically require complete model information, including structural relationships (e.g., how pricing decisions affect customer demand), probabilistic distributions, and parameters. However, in practice, the model information may be uncertain. My dissertation research seeks to address model uncertainty in supply chain management problems using data-driven and robust methods. Incomplete information typically comes in two forms, namely, historical data and partial information. When historical data are available, data-driven methods can be used to obtain decisions directly from data, instead of estimating the model information and then using these estimates to find the optimal solution. When partial information is available, robust methods consider all possible scenarios and make decisions to hedge against the worst-case scenario effectively, instead of making simplified assumptions that could lead to significant loss. Chapter 1 provides an overview of model uncertainty in supply chain management, and discusses the limitations of the traditional methods. The main part of the dissertation is on the application of data-driven and robust methods to three widely-studied supply chain management problems with model uncertainty. Chapter 2 studies the reliable facility location problem where the joint-distribution of facility disruptions is uncertain. For this problem, usually, only partial information in the form of marginal facility disruption probabilities is available. Most existing models require the assumption that the disruptions at different locations are independent of each other. However, in practice, correlated disruptions are widely observed. We present a model that allows disruptions to be correlated with an uncertain joint distribution, and apply distributionally-robust optimization to minimize the expected cost under the worst-case distribution with the given marginal disruption probabilities. The worst-case distribution has a practical interpretation, and its sparse structure allows us to solve the problem efficiently. We find that ignoring disruption correlation could lead to significant loss. The robust method can significantly reduce the regret from model misspecification. It outperforms the traditional approach even under very mild correlation. Most of the benefit of the robust model can be captured at a relatively small cost, which makes it easy to implement in practice. Chapter 3 studies the pricing newsvendor problem where the structural relationship between pricing decisions and customer demand is unknown. Traditional methods for this problem require the selection of a parametric demand model and fitting the model using historical data, while model selection is usually a hard problem in itself. Furthermore, most of the existing literature on pricing requires certain conditions on the demand model, which may not be satisfied by the estimates from data. We present a data-driven approach based only on the historical observations and the basic domain knowledge. The conditional demand distribution is estimated using non-parametric quantile regression with shape constraints. The optimal pricing and inventory decisions are determined numerically using the estimated quantiles. Smoothing and kernelization methods are used to achieve regularization and enhance the performance of the approach. Additional domain knowledge, such as concavity of demand with respect to price, can also be easily incorporated into the approach. Numerical results show that the data-driven approach is able to find close-to-optimal solutions. Smoothing, kernelization, and the incorporation of additional domain knowledge can significantly improve the performance of the approach. Chapter 4 studies inventory management for perishable products where a parameter of the demand distribution is unknown. The traditional separated estimation-optimization approach for this problem has been shown to be suboptimal. To address this issue, an integrated approach called operational statistics has been proposed. We study several important properties of operational statistics. We find that the operational statistics approach is consistent and guaranteed to outperform the traditional approach. We also show that the benefit of using operational statistics is larger when the demand variability is higher. We then generalize the operational statistics approach to the risk-averse newsvendor problem under the conditional value-at-risk (CVaR) criterion. Previous results in operational statistics can be generalized to maximize the expectation of conditional CVaR. In order to model risk-aversion to both the uncertainty in demand sampling and the uncertainty in future demand, we introduce a new criterion called the total CVaR, and find the optimal operational statistic for this new criterion.
This book revises the well-known capacity control problem in revenue management from the perspective of a risk-averse decision-maker. Modelling an expected utility maximizing decision maker, the problem is formulated as a risk-sensitive Markov decision process. Special emphasis is put on the existence of structured optimal policies. Numerical examples illustrate the results.
This book constitutes the refereed proceedings of the 4th International Conference on Big Data and Security, ICBDS 2022, held in Xiamen, China, during December 8–12, 2022. The 51 full papers and 3 short papers included in this book were carefully reviewed and selected from 211 submissions. They were organized in topical sections as follows: answer set programming; big data and new method; intelligence and machine learning security; data technology and network security; sybersecurity and privacy; IoT security.
