Modeling Decision Systems via Uncertain Programming

By uncertain programming we mean the optimization theory in generally uncertain (random, fuzzy, rough, fuzzy random, etc.) environments. The main purpose of this paper is to present a brief review on uncertain programming models, and classify them into three broad classes: expected value model, chanceconstrained programming and dependent-chance programming. This presentation is based on the book: B. Liu, Theory and Practice of Uncertain Programming, PhisicaVerlag, Heidelberg, 200

A Fuzzy Credibility-Based Chance-Constrained Optimization Model for Multiple-Objective Aggregate Production Planning in a Supply Chain under an Uncertain Environment

In this study, a Multiple-Objective Aggregate Production Planning (MOAPP) problem in a supply chain under an uncertain environment is developed. The proposed model considers simultaneously four different conflicting objective functions. To solve the proposed Fuzzy Multiple-Objective Mixed Integer Linear Programming (FMOMILP) model, a hybrid approach has been developed by combining Fuzzy Credibility-based Chance-constrained Programming (FCCP) and Fuzzy Multiple-Objective Programming (FMOP). The FCCP can provide a credibility measure that indicates how much confidence the decision-makers may have in the obtained optimal solutions. In addition, the FMOP, which integrates an aggregation function and a weight-consistent constraint, is capable of handling many issues in making decisions under multiple objectives. The consistency of the ranking of objective’s important weight and satisfaction level is ensured by the weight-consistent constraint. Various compromised solutions, including balanced and unbalanced ones, can be found by using the aggregation function. This methodology offers the decision makers different alternatives to evaluate against conflicting objectives. A case experiment is then given to demonstrate the validity and effectiveness of the proposed formulation model and solution approach. The obtained outcomes can assist to satisfy the decision-makers’ aspiration, as well as provide more alternative strategy selections based on their preferences

The treatment of uncertainty in multicriteria decision making

Bibliography: leaves 142-149.The nature of human decision making dictates that a decision must often be considered under conditions of uncertainty. Decisions may be influenced by uncertain future events, doubts regarding the precision of inputs, doubts as to what the decision maker considers important, and many other forms of uncertainty. The multicriteria decision models that are designed to facilitate and aid decision making must therefore consider these uncertainties if they are to be effective. In this thesis, we consider the treatment of uncertainty in multicriteria decision making (MCDM), with a specific view to investigating the types of uncertainty that are most relevant to MCDM, [and] how the uncertainties identified as relevant may be treated by various different MCDM methodologies

Essays in Robust and Data-Driven Risk Management

Risk defined as the chance that the outcome of an uncertain event is different than expected. In practice, the risk reveals itself in different ways in various applications such as unexpected stock movements in the area of portfolio management and unforeseen demand in the field of new product development. In this dissertation, we present four essays on data-driven risk management to address the uncertainty in portfolio management and capacity expansion problems via stochastic and robust optimization techniques.The third chapter of the dissertation (Portfolio Management with Quantile Constraints) introduces an iterative, data-driven approximation to a problem where the investor seeks to maximize the expected return of his/her portfolio subject to a quantile constraint, given historical realizations of the stock returns. Our approach involves solving a series of linear programming problems (thus) quickly solves the large scale problems. We compare its performance to that of methods commonly used in finance literature, such as fitting a Gaussian distribution to the returns. We also analyze the resulting efficient frontier and extend our approach to the case where portfolio risk is measured by the inter-quartile range of its return. Furthermore, we extend our modeling framework so that the solution calculates the corresponding conditional value at risk CVaR) value for the given quantile level.The fourth chapter (Portfolio Management with Moment Matching Approach) focuses on the problem where a manager, given a set of stocks to invest in, aims to minimize the probability of his/her portfolio return falling below a threshold while keeping the expected portfolio returnno worse than a target, when the stock returns are assumed to be Log-Normally distributed. This assumption, common in finance literature, creates computational difficulties. Because the portfolio return itself is difficult to estimate precisely. We thus approximate the portfolio re-turn distribution with a single Log-Normal random variable by the Fenton-Wilkinson method and investigate an iterative, data-driven approximation to the problem. We propose a two-stage solution approach, where the first stage requires solving a classic mean-variance optimization model, and the second step involves solving an unconstrained nonlinear problem with a smooth objective function. We test the performance of this approximation method and suggest an iterative calibration method to improve its accuracy. In addition, we compare the performance of the proposed method to that obtained by approximating the tail empirical distribution function to a Generalized Pareto Distribution, and extend our results to the design of basket options.The fifth chapter (New Product Launching Decisions with Robust Optimization) addresses the uncertainty that an innovative firm faces when a set of innovative products are planned to be launched a national market by help of a partner company for each innovative product. Theinnovative company investigates the optimal period to launch each product in the presence of the demand and partner offer response function uncertainties. The demand for the new product is modeled with the Bass Diffusion Model and the partner companies\u27 offer response functions are modeled with the logit choice model. The uncertainty on the parameters of the Bass Diffusion Model and the logic choice model are handled by robust optimization. We provide a tractable robust optimization framework to the problem which includes integer variables. In addition, weprovide an extension of the proposed approach where the innovative company has an option to reduce the size of the contract signed by the innovative firm and the partner firm for each product.In the sixth chapter (Log-Robust Portfolio Management with Factor Model), we investigate robust optimization models that address uncertainty for asset pricing and portfolio management. We use factor model to predict asset returns and treat randomness by a budget of uncertainty. We obtain a tractable robust model to maximize the wealth and gain theoretical insights into the optimal investment strategies

Desarrollo de un enfoque de gestión estratégica multiobjetivo para mejorar las decisiones en las prácticas de gestión de pavimentos en las agencias locales

Descargue el texto completo en el repositorio institucional de la Texas A&M University: https://hdl.handle.net/1969.1/ETD-TAMU-1278En este estudio de investigación se desarrolla un enfoque estratégico multiobjetivo para la gestión de pavimentos. La formulación matemática para el problema de asignación de fondos se expresa en términos de objetivos basados en parámetros de desempeño del pavimento a nivel de red. El índice promedio de condición de la red de pavimentos, la vida media remanente de la red de pavimento, el porcentaje de red de pavimento en buenas condiciones y el porcentaje de la red de pavimento en malas condiciones son identificados como parámetros clave de rendimiento de la red de pavimentos. La técnica de la Burbuja Dinámica (Dynamic Bubble-Up - DBU) que se basa en un método de clasificación de orden secuencial en base a criterios de priorización para la asignación de fondos. Las conclusiones de la investigación demuestran la necesidad de proporcionar un enfoque racional coherente con los objetivos de las agencias. También se concluye en este estudio que los tratamientos de mantenimiento preventivo aplicados en el momento oportuno reducen las necesidades futuras de inversión aumentando la eficiencia de los programas de gestión.Multiple objectives are often used by agencies trying to manage pavement networks. Often alternative investment strategies can accomplish the agencies’ target objectives. If the goal is to achieve the target objectives at the minimum cost, an approach is needed to assist agencies in identifying investment strategies capable of meeting the targets while minimizing costs. The approach used by the agency should not be limited to an analytical method to mathematically solve the funding allocation problem. Finding mechanisms to ensure the sustainability and efficiency of the investment strategy over time is a great challenge that needs to be addressed by the approach. The challenge is even greater for local agencies where resources are usually limited. This research develops a multi-objective strategic management approach oriented to improving decisions for pavement management practices in local agencies. In this approach, target objectives are tied to key pavement network parameters in the management process. A methodology to identify the best combination of projects to meet target objectives at the minimum cost while maximizing treatment effectiveness is provided as a result of the research. Concepts from the pavement management program (PMP) of the Metropolitan Transportation Commission (MTC) of the San Francisco Bay Area were used as a basis for developing the methodology. Four pavement network parameters are considered for setting the target objectives over the agency’s planning horizon: the average network pavement condition index (PCI), average network remaining life, percent of the pavement network in good condition, and percent of the pavement network in poor and very poor condition. Results from a case study show that funding allocation methods influence the allocation of preservation and rehabilitation funds among pavement network groups, affecting budget estimates and future condition of the pavement network. It is also concluded that the use of mechanisms that facilitate data integration and the flow of knowledge across management levels can contribute to making better informed decisions. Hence, the adoption of the multi-objective strategic pavement management approach developed in this dissertation should lead to identifying more efficient investment strategies for achieving the pavement network state desired by a local agency at a minimum cost

Conflicting Objectives in Decisions

This book deals with quantitative approaches in making decisions when conflicting objectives are present. This problem is central to many applications of decision analysis, policy analysis, operational research, etc. in a wide range of fields, for example, business, economics, engineering, psychology, and planning. The book surveys different approaches to the same problem area and each approach is discussed in considerable detail so that the coverage of the book is both broad and deep. The problem of conflicting objectives is of paramount importance, both in planned and market economies, and this book represents a cross-cultural mixture of approaches from many countries to the same class of problem