This book presents a structured approach to formulate, model, and solve mathematical optimization problems for a wide range of real world situations. Among the problems covered are production, distribution and supply chain planning, scheduling, vehicle routing, as well as cutting stock, packing, and nesting. The optimization techniques used to solve the problems are primarily linear, mixed-integer linear, nonlinear, and mixed integer nonlinear programming. The book also covers important considerations for solving real-world optimization problems, such as dealing with valid inequalities and symmetry during the modeling phase, but also data interfacing and visualization of results in a more and more digitized world. The broad range of ideas and approaches presented helps the reader to learn how to model a variety of problems from process industry, paper and metals industry, the energy sector, and logistics using mathematical optimization techniques.

This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.

Here is a collection of nonlinear optimization applications from the real world, expressed in the General Algebraic Modeling System (GAMS). The concepts are presented so that the reader can quickly modify and update them to represent real-world situations.

This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.

This textbook offers a comprehensive, up-to-date introduction to the Optimization Programming Language (OPL). Embedded in the IBM ILOG CPLEX Optimization Studio with its solver engine CPLEX, OPL has been popular for years not only for academic and scientific purposes, but also among practitioners who need to model and solve large-scale real-world business optimization problems. The book covers the recent features of the software and includes ten consecutive tutorials, each with additional exercises, as well as several comprehensive application studies. The book is specifically designed for advanced undergraduate and graduate courses in e.g. management science, operations research, computer science, mathematics, mathematical economics, and industrial engineering. It can also serve as self-study material for practitioners whose work involves the modeling and optimization of planning and decision problems and who need a sound introduction to the software. Solutions to the exercises as well as the source codes from the textbook are available for download (weblink included).

As the age of Big Data emerges, it becomes necessary to take the five dimensions of Big Data- volume, variety, velocity, volatility, and veracity- and focus these dimensions towards one critical emphasis - value. The Encyclopedia of Business Analytics and Optimization confronts the challenges of information retrieval in the age of Big Data by exploring recent advances in the areas of knowledge management, data visualization, interdisciplinary communication, and others. Through its critical approach and practical application, this book will be a must-have reference for any professional, leader, analyst, or manager interested in making the most of the knowledge resources at their disposal.

Energy is one of the world`s most challenging problems, and power systems are an important aspect of energy related issues. This handbook contains state-of-the-art contributions on power systems modeling and optimization. The book is separated into two volumes with six sections, which cover the most important areas of energy systems. The first volume covers the topics operations planning and expansion planning while the second volume focuses on transmission and distribution modeling, forecasting in energy, energy auctions and markets, as well as risk management. The contributions are authored by recognized specialists in their fields and consist in either state-of-the-art reviews or examinations of state-of-the-art developments. The articles are not purely theoretical, but instead also discuss specific applications in power systems.

This book gathers a selection of peer-reviewed papers presented at the International Conference on Operations Research (OR 2022), which was held at Karlsruhe Institute of Technology, Germany, on September 6-9, 2022. KIT’s Institute for Operations Research (IOR) hosted the conference together with the Institute for Industrial Production (IIP), the Institute for Automation and Applied Informatics (IAI), and the Institute for Material Handling and Logistics (IFL). The respective papers discuss classical mathematical optimization, statistics and simulation techniques. These are complemented by computer science methods, and by tools for processing data, designing and implementing information systems. The book also examines recent advances in information technology, which allow big data volumes to be processed and enable real-time predictive and prescriptive business analytics to drive decisions and actions. Lastly, it includes problems modeled and treated while taking into account uncertainty, risk management, behavioral issues, etc.

The contributions included in the volume are drawn from presentations at ODS2019 – International Conference on Optimization and Decision Science, which was the 49th annual meeting of the Italian Operations Research Society (AIRO) held at Genoa, Italy, on 4-7 September 2019. This book presents very recent results in the field of Optimization and Decision Science. While the book is addressed primarily to the Operations Research (OR) community, the interdisciplinary contents ensure that it will also be of very high interest for scholars and researchers from many scientific disciplines, including computer sciences, economics, mathematics, and engineering. Operations Research is known as the discipline of optimization applied to real-world problems and to complex decision-making fields. The focus is on mathematical and quantitative methods aimed at determining optimal or near-optimal solutions in acceptable computation times. This volume not only presents theoretical results but also covers real industrial applications, making it interesting for practitioners facing decision problems in logistics, manufacturing production, and services. Readers will accordingly find innovative ideas from both a methodological and an applied perspective.

A practical guide to using Excel for decision making, forecasting, optimization, and more KEY FEATURES ● Solve a wide range of decision-making problems in operations, finance, and statistics. ● Build and use Excel models to analyze data and make informed decisions. ● Use the Excel Solve function to find the optimal solution to a problem. DESCRIPTION This book on management science serves as a valuable resource for enhancing problem-solving and decision-making skills across various domains, including organizations and business. By reading this book, you will acquire the ability to tackle complex decisions that would otherwise be challenging. The book covers a wide array of techniques, such as profit and performance maximization, Return on Investment (ROI) optimization, as well as cost, time, and risk minimization through tools like Monte Carlo simulations and sensitivity analysis. Throughout the book, you'll come across numerous real-life examples and case studies from diverse fields such as banking, finance, transportation, manufacturing, manpower assignment, scheduling, inventory management, and even food and product mix. The book demonstrates both linear and nonlinear techniques, utilizing Excel Solver for finding solutions. Once you grasp the usage of Solver, you'll be able to apply the learned tools effectively to address problems relevant to your background, experience, and preferences. What sets this book apart is its hands-on approach, leveraging Excel as the primary tool for problem-solving. Rather than relying on complex mathematical formulations and algorithms, you'll learn how to set up and solve problems in a straightforward manner using Excel. WHAT YOU WILL LEARN ● Learn how to set up decision making models on Excel. ● Solve optimization problems in the areas of business and operations. ● Harness the power of the Excel Solver add-in. ● Apply Monte Carlo simulations of risky investments using Excel. ● Learn how to predict future values using Excel forecasting features. WHO THIS BOOK IS FOR This book is for any business or operations practitioner, regardless of their role or experience level. Whether you are an analyst, a business professional, or a student, this book can help you to improve your problem-solving and decision-making skills. TABLE OF CONTENTS 1. Making Better Decisions with Management Science 2. Exploring Management Science Optimization Techniques 3. Unleash the Power of Excel’s Solver for Optimizations 4. Optimize Product Mix 5. Investment and Portfolio Optimization with Excel’s Solver 6. The Assignment Problem Challenges and Solutions 7. Solving Transportation Supply Chain Problems 8. Marketing Applications of Optimal Media Mix 9. Integer and Binary Optimization 10. The Scheduling Puzzle 11. Nonlinear Optimization Applied to Inventory and Facility Location 12. Monte Carlo Simulations 13. Simplifying Forecasting Using Excel’s Forecast Sheet Feature 14. Queuing and Waiting Time