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Mechanism design : a linear programming approach
\"Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design\"-- Provided by publisher.
Book
Mechanism Design
Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design.
eBook
Mechanism design : a linear programming approach
\"Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design\"--
Book
Robust Optimization
Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.
eBook
Adaptive Distributionally Robust Optimization
We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an
ambiguity set
of probability distributions. The adaptive distributionally robust optimization framework caters for dynamic decision making, where decisions adapt to the uncertain outcomes as they unfold in stages. For tractability considerations, we focus on a class of second-order conic (SOC) representable ambiguity set, though our results can easily be extended to more general conic representations. We show that the adaptive distributionally robust linear optimization problem can be formulated as a classical robust optimization problem. To obtain a tractable formulation, we approximate the adaptive distributionally robust optimization problem using linear decision rule (LDR) techniques. More interestingly, by incorporating the primary and auxiliary random variables of the lifted ambiguity set in the LDR approximation, we can significantly improve the solutions, and for a class of adaptive distributionally robust optimization problems, exact solutions can also be obtained. Using the new LDR approximation, we can transform the distributionally adaptive robust optimization problem to a classical robust optimization problem with an SOC representable uncertainty set. Finally, to demonstrate the potential for solving management decision problems, we develop an algebraic modeling package and illustrate how it can be used to facilitate modeling and obtain high-quality solutions for medical appointment scheduling and inventory management problems.
The electronic companion is available at
https://doi.org/10.1287/mnsc.2017.2952
.
This paper was accepted by Noah Gans, optimization.
Journal Article
Deep Reinforcement Learning-Based Task Scheduling in IoT Edge Computing
Edge computing (EC) has recently emerged as a promising paradigm that supports resource-hungry Internet of Things (IoT) applications with low latency services at the network edge. However, the limited capacity of computing resources at the edge server poses great challenges for scheduling application tasks. In this paper, a task scheduling problem is studied in the EC scenario, and multiple tasks are scheduled to virtual machines (VMs) configured at the edge server by maximizing the long-term task satisfaction degree (LTSD). The problem is formulated as a Markov decision process (MDP) for which the state, action, state transition, and reward are designed. We leverage deep reinforcement learning (DRL) to solve both time scheduling (i.e., the task execution order) and resource allocation (i.e., which VM the task is assigned to), considering the diversity of the tasks and the heterogeneity of available resources. A policy-based REINFORCE algorithm is proposed for the task scheduling problem, and a fully-connected neural network (FCN) is utilized to extract the features. Simulation results show that the proposed DRL-based task scheduling algorithm outperforms the existing methods in the literature in terms of the average task satisfaction degree and success ratio.
Journal Article
Reverse logistics optimization of an industrial air conditioner manufacturing company for designing sustainable supply chain: a fuzzy hybrid multi-criteria decision-making approach
Magnified resource consumption and depletion of natural resources calls for non-flexible or strict regulations and penalties on industrial operations, increased rate of processing and reuse of waste material as a substitute for raw material and political and legal interventions at global scale. Product recovery involves reuse, repair, refurbishing, remanufacturing and materials recycling, requires an efficient network design known as reverse logistic network and offers economical benefits in terms of fewer procurement of raw material, inventory management and less disposal. In current study, a mixed integer linear programming model designed on a multi-stage reverse logistics network for product recovery is proposed which considers different recovery options-product remanufacturing, component reprocessing and material recycling for sustainable outcomes. The model is designed to find optimal solutions for fulfilling demand and revenue needs by focusing on strategic locations for collection centers, reprocessing centers, remanufacturing plants and transportation options and simultaneously achieving sustainability goals. The model is applied on an Indian based manufacturing unit of a Saudi Arabian Industrial Air conditioner manufacturing organization and the case is presented here. The model is converted into a multi-objective programming model in accordance with the importance of each objective suiting the business needs. All relevant objective functions are evaluated using BWM, AHP and FAHP methods to obtain weights for integration into a fuzzy linear programming model which eventually provides three separate results. The model applied has originality and uniqueness for applications to solve multi-objective problems under uncertain environment and tends to strike a balance between economic and environmental objectives. The study provides for a base for further scope covering uncertainty about the amount and quality of returned products and even can be implemented by practitioners and academics for making a significant contribution in improving the efficiency of supply chains.
Journal Article
A review on TOPSIS method and its extensions for different applications with recent development
The main objective of the study is to review different types of multi-criteria decision-making (MCDM) problems that are analysed by using the fuzzy TOPSIS method and its different variants. An effort has been made to review different studies in which either the TOPSIS method is used or its extensions have been developed to analyse any real-life MCDM problem. A total of 184 research papers were carefully selected and reviewed from 83 reputed journals published by Elsevier, Springer, Wiley, Taylor and Francis, and others from 1981 to the first quarter of 2023. These papers are selected on the basis of different kinds of applications in the fields of mathematics, engineering, science, environment, technology, management, business, etc. The selected papers are further categorised based on the application areas, publication year, contributions of the countries, authors, journals, and type of research. This study will give an idea of different types of TOPSIS methods, their extensions, and applications, along with recent trends in diverse research fields. Based on the findings, it is observed that in recent years, the number of papers in which TOPSIS and its extensions have been used has increased exponentially.
Journal Article
Green supplier selection and order allocation in a low-carbon paper industry: integrated multi-criteria heterogeneous decision-making and multi-objective linear programming approaches
The low-carbon supply chain is one of the predominant topics towards a green economy and it establishes the opportunity to reduce carbon emissions across the product value chain. This paper focuses on recycling and optimized sourcing in the paper industry as a case company. The main objective is to engage the case company with their supplier networks to diminish the greenhouse gases (GHG) emissions and cost in their production process. It proposes a model to support the selection of the best green supplier and an allocation of order among the potential suppliers. The proposed model contains a two-phase hybrid approach. The first phase presents the rating and selection of potential suppliers by considering economics (cost), operational factors (quality and delivery), and environmental criteria (recycle capability and GHG emission control) using Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS) methodology. The second phase presents the order allocation process using multi-objective linear programming in order to minimize cost, material rejection, late delivery, recycle waste and
CO
2
emissions in the production process. A case study from a paper manufacturing industry is presented to elucidate the effectiveness of the proposed model. The results demonstrate a 26.2 % reduction of carbon emission by using recycle products in the production process. The firm benefits by forming a systematic methodology for green supplier evaluation and order allocation. Finally, a conclusion and a suggested direction of future research are introduced.
Journal Article
Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey
To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization model and the computational time required to solve it. This motivates the scientific community to develop efficient transformation and linearization approaches for the optimization models that have non-linear terms. Such transformations and linearizations are expected to decrease the computational complexity of the original non-linear optimization models and, ultimately, facilitate decision making. This study provides a detailed state-of-the-art review focusing on the existing transformation and linearization techniques that have been used for solving optimization models with non-linear terms within the objective functions and/or constraint sets. The existing transformation approaches are analyzed for a wide range of scenarios (multiplication of binary variables, multiplication of binary and continuous variables, multiplication of continuous variables, maximum/minimum operators, absolute value function, floor and ceiling functions, square root function, and multiple breakpoint function). Furthermore, a detailed review of piecewise approximating functions and log-linearization via Taylor series approximation is presented. Along with a review of the existing methods, this study proposes a new technique for linearizing the square root terms by means of transformation. The outcomes of this research are anticipated to reveal some important insights to researchers and practitioners, who are closely working with non-linear optimization models, and assist with effective decision making.
Journal Article