Stefan Voß

David L. Woodruff

provide models that could be used by do-it-yourselfers and also can be used toprovideunderstandingofthebackgroundissuessothatonecandoabetter job of working with the (proprietary) algorithms of the software vendors. In this book we strive to provide models that capture many of the - tails faced by ?rms operating in a modern supply chain, but we stop short of proposing models for economic analysis of the entire multi-player chain. In other words, we produce models that are useful for planning within a supply chain rather than models for planning the supply chain. The usefulness of the models is enhanced greatly by the fact that they have been implemented - ing computer modeling languages. Implementations are shown in Chapter 7, which allows solutions to be found using a computer. A reasonable question is: why write the book now? It is a combination of opportunities that have recently become available. The availability of mod- inglanguagesandcomputersthatprovidestheopportunitytomakepractical use of the models that we develop. Meanwhile, software companies are p- viding software for optimized production planning in a supply chain. The opportunity to make use of such software gives rise to a need to understand some of the issues in computational models for optimized planning. This is best done by considering simple models and examples.

Introduction to Computational Optimization Models for Production Planning in a Supply Chain

Jean-Paul Watson

William E. Hart

Carl Laird

This book provides a complete and comprehensive reference/guide to Pyomo (Python Optimization Modeling Objects) for both beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. The text illustrates the breadth of the modeling and analysis capabilities that are supported by the software and support of complex real-world applications. Pyomo is an open source software package for formulating and solving large-scale optimization and operations research problems. The text begins with a tutorial on simple linear and integer programming models. A detailed reference of Pyomo's modeling components is illustrated with extensive examples, including a discussion of how to load data from data sources like spreadsheets and databases. Chapters describing advanced modeling capabilities for nonlinear and stochastic optimization are also included. The Pyomo software provides familiar modeling features within Python, a powerful dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions. The software supports a different modeling approach than commercial AML (Algebraic Modeling Languages) tools, and is designed for flexibility, extensibility, portability, and maintainability but also maintains the central ideas in modern AMLs.

Pyomo – Optimization Modeling in Python

Michael L. Bynum

Gabriel A. Hackebeil

Carl D. Laird

Bethany L. Nicholson

John D. Siirola

This book provides a complete and comprehensive guide to Pyomo (Python Optimization Modeling Objects) for beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. Using many examples to illustrate the different techniques useful for formulating models, this text beautifully elucidates the breadth of modeling capabilities that are supported by Pyomo and its handling of complex real-world applications. In the third edition, much of the material has been reorganized, new examples have been added, and a new chapter has been added describing how modelers can improve the performance of their models. The authors have also modified their recommended method for importing Pyomo. A big change in this edition is the emphasis of concrete models, which provide fewer restrictions on the specification and use of Pyomo models. Pyomo is an open source software package for formulating and solving large-scale optimization problems. The software extends the modeling approach supported by modern AML (Algebraic Modeling Language) tools. Pyomo is a flexible, extensible, and portable AML that is embedded in Python, a full-featured scripting language. Python is a powerful and dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions.

Pyomo — Optimization Modeling in Python

​This book provides a complete and comprehensive guide to Pyomo (Python Optimization Modeling Objects) for beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. Using many examples to illustrate the different techniques useful for formulating models, this text beautifully elucidates the breadth of modeling capabilities that are supported by Pyomo and its handling of complex real-world applications. This second edition provides an expanded presentation of Pyomo’s modeling capabilities, providing a broader description of the software that will enable the user to develop and optimize models. Introductory chapters have been revised to extend tutorials; chapters that discuss advanced features now include the new functionalities added to Pyomo since the first edition including generalized disjunctive programming, mathematical programming with equilibrium constraints, and bilevel programming. Pyomo is an open source software package for formulating and solving large-scale optimization problems. The software extends the modeling approach supported by modern AML (Algebraic Modeling Language) tools. Pyomo is a flexible, extensible, and portable AML that is embedded in Python, a full-featured scripting language. Python is a powerful and dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions.

Computer Science and Operations Research continue to have a synergistic relationship and this book - as a part of the Operations Research and Computer Science Interface Series - sits squarely in the center of the confluence of these two technical research communities. The research presented in the volume is evidence of the expanding frontiers of these two intersecting disciplines and provides researchers and practitioners with new work in the areas of logic programming, stochastic optimization, heuristic search and post-solution analysis for integer programs. The chapter topics span the spectrum of application level. Some of the chapters are highly applied and others represent work in which the application potential is only beginning. In addition, each chapter contains expository material and reviews of the literature designed to enhance the participation of the reader in this expanding interface.

Interfaces in Computer Science and Operations Research

Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search

Optimization problems in practice are diverse and evolve over time, giving rise to - quirements both for ready-to-use optimization software packages and for optimization software libraries, which provide more or less adaptable building blocks for app- cation-specific software systems. In order to apply optimization methods to a new type of problem, corresponding models and algorithms have to be “coded” so that they are accessible to a computer. One way to achieve this step is the use of a mod- ing language. Such modeling systems provide an excellent interface between models and solvers, but only for a limited range of model types (in some cases, for example, linear) due, in part, to limitations imposed by the solvers. Furthermore, while m- eling systems especially for heuristic search are an active research topic, it is still an open question as to whether such an approach may be generally successful. Modeling languages treat the solvers as a “black box” with numerous controls. Due to variations, for example, with respect to the pursued objective or specific problem properties, - dressing real-world problems often requires special purpose methods. Thus, we are faced with the difficulty of efficiently adapting and applying appropriate methods to these problems. Optimization software libraries are intended to make it relatively easy and cost effective to incorporate advanced planning methods in application-specific software systems. A general classification provides a distinction between callable packages, nume- cal libraries, and component libraries.

David L. Woodruff

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