Optimization Models

This accessible textbook demonstrates how to recognize, simplify, model and solve optimization problems - and apply these principles to new projects.

This concise text contains the most commonly-encountered examination problems in the topic of Optimization Models and Methods, an important module in engineering and other disciplines where there exists an increasing need to operate optimally and sustainably under constraints, such as tighter resource availability, environmental consideration, and cost pressures. This book is comprehensive in coverage as it includes a diverse spectrum of problems from numerical open-ended questions that probe creative thinking to the relation of concepts to realistic settings. The book adopts many examples of design scenarios as context for curating sample problems. This will help students relate desktop problem-solving to tackling real-world problems. Succinct yet rigorous, with over a 100 pages of problems and corresponding worked solutions presented in detail, the book is ideal for students of engineering, applied science, and market analysis.

Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered in transportation and communication. Marketing models use stochastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain stochastic processes, and insurance claims appear at random times with random amounts. To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined. The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated. Optimization of Stochastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Stochastic Models or as a secondary text for a graduate level course in Operations Research.

A reference for those working at the interface of operations planning and optimization modeling, Operations Planning: Mixed Integer Optimization Models blends essential theory and powerful approaches to practical operations planning problems. It presents a set of classical optimization models with widespread application in operations planning. The

Network models are critical tools in business, management, science and industry. “Network Models and Optimization” presents an insightful, comprehensive, and up-to-date treatment of multiple objective genetic algorithms to network optimization problems in many disciplines, such as engineering, computer science, operations research, transportation, telecommunication, and manufacturing. The book extensively covers algorithms and applications, including shortest path problems, minimum cost flow problems, maximum flow problems, minimum spanning tree problems, traveling salesman and postman problems, location-allocation problems, project scheduling problems, multistage-based scheduling problems, logistics network problems, communication network problem, and network models in assembly line balancing problems, and airline fleet assignment problems. The book can be used both as a student textbook and as a professional reference for practitioners who use network optimization methods to model and solve problems.

An easy-to-read introduction to the concepts associated with the creation of optimization models for production planning starts off this book. These concepts are then applied to well-known planning models, namely mrp and MRP II. From this foundation, fairly sophisticated models for supply chain management are developed. Another unique feature is that models are developed with an eye toward implementation. In fact, there is a chapter that provides explicit examples of implementation of the basic models using a variety of popular, commercially available modeling languages.

In this book . . . Nicolas Vandeput hacks his way through the maze of quantitative supply chain optimizations. This book illustrates how the quantitative optimization of 21st century supply chains should be crafted and executed. . . . Vandeput is at the forefront of a new and better way of doing supply chains, and thanks to a richly illustrated book, where every single situation gets its own illustrating code snippet, so could you. --Joannes Vermorel, CEO, Lokad Inventory Optimization argues that mathematical inventory models can only take us so far with supply chain management. In order to optimize inventory policies, we have to use probabilistic simulations. The book explains how to implement these models and simulations step-by-step, starting from simple deterministic ones to complex multi-echelon optimization. The first two parts of the book discuss classical mathematical models, their limitations and assumptions, and a quick but effective introduction to Python is provided. Part 3 contains more advanced models that will allow you to optimize your profits, estimate your lost sales and use advanced demand distributions. It also provides an explanation of how you can optimize a multi-echelon supply chain based on a simple—yet powerful—framework. Part 4 discusses inventory optimization thanks to simulations under custom discrete demand probability functions. Inventory managers, demand planners and academics interested in gaining cost-effective solutions will benefit from the "do-it-yourself" examples and Python programs included in each chapter. Events around the book Link to a De Gruyter Online Event in which the author Nicolas Vandeput together with Stefan de Kok, supply chain innovator and CEO of Wahupa; Koen Cobbaert, Director in the S&O Industry practice of PwC Belgium; Bram Desmet, professor of operations & supply chain at the Vlerick Business School in Ghent; and Karl-Eric Devaux, Planning Consultant, Hatmill, discuss about models for inventory optimization. The event will be moderated by Eric Wilson, Director of Thought Leadership for Institute of Business Forecasting (IBF): https://youtu.be/565fDQMJEEg

This textbook covers the fundamentals of optimization, including linear, mixed-integer linear, nonlinear, and dynamic optimization techniques, with a clear engineering focus. It carefully describes classical optimization models and algorithms using an engineering problem-solving perspective, and emphasizes modeling issues using many real-world examples related to a variety of application areas. Providing an appropriate blend of practical applications and optimization theory makes the text useful to both practitioners and students, and gives the reader a good sense of the power of optimization and the potential difficulties in applying optimization to modeling real-world systems. The book is intended for undergraduate and graduate-level teaching in industrial engineering and other engineering specialties. It is also of use to industry practitioners, due to the inclusion of real-world applications, opening the door to advanced courses on both modeling and algorithm development within the industrial engineering and operations research fields.