Download or read book On Risk averse and Robust Inventory Problems written by Ulas Cakmak and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Robustness Analysis in Decision Aiding Optimization and Analytics written by Michael Doumpos and published by Springer. This book was released on 2016-07-12 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Models in Reliability Network Security and System Safety written by Quan-Lin Li and published by Springer Nature. This book was released on 2019-10-21 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Operational Research written by João Paulo Almeida and published by Springer Nature. This book was released on 2024-01-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on Stochastic Programming written by Alexander Shapiro and published by SIAM. This book was released on 2014-07-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Solving Robust Inventory Problems written by Nuri Sercan Özbay and published by . This book was released on 2006 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essays on Supply Chain Management with Model Uncertainty written by Mengshi Lu and published by . This book was released on 2014 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Risk Averse Capacity Control in Revenue Management written by Christiane Barz and published by Springer Science & Business Media. This book was released on 2007-08-16 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Big Data and Security written by Yuan Tian and published by Springer Nature. This book was released on 2023-05-30 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applications of Stochastic Inventory Control in Market making and Robust Supply Chains written by Miao Song (Ph. D.) and published by . This book was released on 2010 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation extends the classical inventory control model to address stochastic inventory control problems raised in market-making and robust supply chains. In the financial market, market-makers assume the role of a counterpart so that investors can trade any fixed amounts of assets at quoted bid or ask prices at any time. Market-makers benefit from the spread between the bid and ask prices. but they have to carry inventories of assets which expose them to potential losses when the market price moves in an undesirable direction. One approach to reduce the risk associated with price uncertainty is to actively trade with other Market-Makers at the price of losing potential spread gain. We propose a dynamic programming model to determine the optimal active trading quantity., which maximizes the Market-Maker's expected utility. For a single-asset model. we show that a threshold inventory control policy is optimal with respect to both an exponential utility criterion and a mean-variance tradeoff objective. Special properties such as symmetry and monotonicity of the threshold levels are also investigated. For a multiple-asset model. the mean-variance analysis suggests that there exists a connected no-trade region such that the Market-Maker does not need to actively trade with other market-makers if the inventory falls in the no-trade region. Outside the no-trade region. the optimal way to adjust inventory levels can be obtained from the boundaries of the no-trade region. These properties of the optimal policy lead to practically efficient algorithms to solve the problem. The dissertation also considers the stochastic inventory control model in robust supply chain systems. Traditional approaches in inventory control first estimate the demand distribution among a predefined family of distributions based on data fitting of historical demand observations, and then optimize the inventory control policy using the estimated distributions. which often leads to fragile solutions in case the preselected family of distributions was inadequate. In this work. we propose a minimax robust model that integrates data fitting and inventory optimization for the single item multi-period periodic review stochastic lot-sizing problem. Unlike the classical stochastic inventory models, where demand distribution is known, we assume that histograms are part of the input. The robust model generalizes Bayesian model, and it can be interpreted as minimizing history dependent risk measures. We prove that the optimal inventory control policies of the robust model share the same structure as the traditional stochastic dynamic programming counterpart. In particular., we analyze the robust models based on the chi-square goodness-of-fit test. If demand samples are obtained from a known distribution, the robust model converges to the stochastic model with true distribution under general conditions.
Download or read book Dynamic Inventory Optimization with Learning and Model Ambiguity written by Ya-Tang Chuang and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic inventory control problems typically assume that the demand distribution is known a priori. In reality, this assumption is not always satisfied. Motivated by this concern, the joint optimization of learning and control is studied. We first consider the situation where parameters of the demand distribution are not known a priori, but need to be learned using right-censored sales data. A Bayesian framework is adopted for demand learning and the corresponding control problem is analyzed via Bayesian dynamic programming (BDP). Structural results of the optimal policy are established. In particular, we show that the BDP-optimal decisions can be expressed as the sum of a myopic-optimal decision plus a non-negative exploration boost which is proportional to the posterior index of dispersion of the unknown mean demand. This structure clearly articulates the manner in which the statistical learning and inventory control are jointly optimized. Next, we study an optimal inventory control problem in the presence of model miss-specification. In this problem, decision makers account for the miss-specification via solving a worst-case problem against an adversary, ``nature", who has the ability to alter the underlying demand distribution so as to minimize the decision maker's expected reward. We show that the decision maker's robust-optimal decisions are bounded above by the optimal solutions of the nominal model. This structural result clearly explains the trade-off between optimization and risk aversion. In the last chapter, we attempt to incorporate the elements of the Bayesian and robust approaches, namely robust Bayesian optimization. In particular, we are interested in how decision makers can remain robust to model uncertainty while also learning at the same time. We establish an analytical upper bound of the decision maker's optimal decisions, which can be expressed as the sum of a myopic-optimal decision plus an exploration boost and minus a risk aversion adjustment. We then propose a heuristic which is based on the approximation of the first order optimality condition, and the effort of computing this heuristic solution is essentially equal to obtain the robust-optimal and BDP-optimal solutions separately.
Download or read book Analyzing Risk through Probabilistic Modeling in Operations Research written by Jakóbczak, Dariusz Jacek and published by IGI Global. This book was released on 2015-11-03 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic modeling represents a subject spanning many branches of mathematics, economics, and computer science to connect pure mathematics with applied sciences. Operational research also relies on this connection to enable the improvement of business functions and decision making. Analyzing Risk through Probabilistic Modeling in Operations Research is an authoritative reference publication discussing the various challenges in management and decision science. Featuring exhaustive coverage on a range of topics within operational research including, but not limited to, decision analysis, data mining, process modeling, probabilistic interpolation and extrapolation, and optimization methods, this book is an essential reference source for decision makers, academicians, researchers, advanced-level students, technology developers, and government officials interested in the implementation of probabilistic modeling in various business applications.
Download or read book Facility Location Under Uncertainty written by Francisco Saldanha-da-Gama and published by Springer Nature. This book was released on with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Improved Models and Algorithms for Robust Inventory Problems with Static and Basestock Policies written by Oğuz Solyali and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Programming written by Horand Gassmann and published by World Scientific. This book was released on 2013 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.
Download or read book Scheduling Inventory Management and Production Planning written by Pedram Hooshangitabrizi and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents formulations and solution methods for three types of problems in operations management that have received major attention in the last decade and arise in several applications. We focus on the use of mixed integer programming theory, robust optimization, and decomposition-based methods to solve each of these three problems. We first study an online scheduling problem dealing with patients' multiple requests for chemotherapy treatments. We propose an adaptive and flexible scheduling procedure capable of handling both the dynamic uncertainty arising from appointment requests that appear on waiting lists in real time and capable of dealing with unexpected changes. The proposed scheduling procedure incorporates several circumstances prevalent at oncology clinics such as specific intervals between two consecutive appointments and specific time slots and chairs. Computational experiments show the proposed procedure achieves consistently better results for all considered objective functions compared to those of the scheduling system in use at the cancer centre of a major metropolitan hospital in Canada. We next present an inventory management problem that integrates perishability, demand uncertainty, and order modification decisions. We formulate the problem as a two-stage robust integer optimization model and develop an exact column-and-row generation algorithm to solve it. Based on computational results, we show that considering order modification can significantly reduce the total cost. Moreover, comparing the results obtained by the proposed robust model to those obtained from the deterministic and stochastic variants, we note that their performances are similar in the risk-neutral setting while solutions from the robust models are significantly superior in the risk-averse setting. Finally, we study decomposition strategies for a class of production planning problems with multiple items, unlimited production capacity and, inventory bounds. Based on a new mixed integer programming formulation, we proposed a Lagrangian relaxation for the problem. We propose a deflected subgradient method and a stabilized column generation algorithm to solve the Lagrangian dual problem. Computational results confirm that the proposed formulation outperforms the previously proposed models and methods. Further analysis shows the impact of using decomposition techniques in providing tighter bounds.
Download or read book Distributionally Robust Inventory Management with Advance Purchase Contracts written by Yilin Xue and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a distributionally robust inventory model for finding an optimal ordering policy that attains the minimum worst-case expected total cost. In a classical stochastic setting, this problem is typically addressed by dynamic programming and is solved by the famous base-stock policy. This approach however crucially relies on two controversial assumptions: the demands are serially independent and the demand distribution is perfectly known. Aiming to address these issues, inspired by the seminal work of Scarf (1958), we adopt a mean-variance ambiguity set that imposes neither the shape of each marginal demand distribution nor their independence structure, and we focus on the case of advance purchase agreements which are prevalent in the robust inventory literature and have drawn renewed attention because of the Covid-19 vaccine procurement. The proposed distributionally robust inventory model provably reduces to a finite conic optimization problem with however an exponential number of constraints. To gain tractability and to err on the safe side, we propose two conservative approximations. The first approximation is obtained by recognizing the problem as an artificial two-stage robust optimization problem and then by restricting each adaptive decision to a linear decision rule. The second approximation, on the other hand, is obtained by a constraint partitioning and by upper bounding each resultant maximum sum with a sum of maxima. We then present a progressive approximation based on a scenario reduction technique to gauge the quality of the proposed conservative approximations. We prove that this progressive approximation is exact when the inventory problem consists of two periods, and besides we use it to show that our conservative solutions are still close to being optimal when the planning horizon is longer. All of our exact and approximate inventory models are expressed as standard conic programs which allow for the incorporation of additional distributional information. The extensions are readily obtained by deriving a new cone that corresponds to the restricted ambiguity set and embedding it in the original problems. We analytically derive the worst-case demand distribution from the mean-variance ambiguity set and numerically use it to show that our robust inventory policy is more resilient to the misspecification of the demand distribution than the state-of-the-art non-robust policies.
