8 Linear Programming Books That Define the Field

What started as a challenge to connect economic theory with practical optimization techniques became this influential text by Robert Dorfman, Paul Samuelson, and Robert Solow. Drawing on their distinct expertise, they explore how linear programming methods can be applied to economic analysis, offering readers insights into production optimization, cost minimization, and resource allocation. The book delves into mathematical formulations while maintaining accessibility, making it suitable for economists aiming to enhance quantitative skills and mathematicians interested in economic applications. You’ll find detailed discussions on duality theory and shadow pricing that illuminate economic decision-making processes.

What if everything you knew about linear programming was wrong? Saul I. Gass, a seasoned authority in operations research, presents a methodical exploration of linear programming that goes beyond typical treatments. You’ll gain insight into both theoretical frameworks and computational techniques, including the simplex and revised simplex methods, along with a rich set of examples and exercises to sharpen your skills. This book suits anyone aiming to deepen their understanding of optimization models and their applications, especially in academic or professional settings where precision and rigor matter.

This tailored book offers a deep dive into linear programming, exploring both its fundamental principles and diverse applications with clarity and focus. It reveals how linear programming optimizes decisions in various fields by modeling constraints and objectives mathematically. The book takes a personalized approach, crafting content that matches your background and interests while addressing your specific goals. You’ll engage with tailored explanations that unpack complex concepts like simplex methods, duality, and sensitivity analysis, ensuring your learning aligns with your unique path. This personalized guide transforms expert knowledge into an accessible and engaging learning journey, making linear programming both understandable and applicable for you.

After years immersed in operations research and optimization, Matteo Fischetti crafted this book to clarify complex topics like linear and integer linear programming for scientific students. The text drills down into computational complexity, graph theory, and especially recent advances like the branch-and-cut method for integer programming. You’ll find numerous examples and exercises designed to deepen your grasp of these mathematical tools. This book suits those who want a solid foundation in optimization methods, particularly if you’re tackling integer programming techniques as part of your studies or research.

After analyzing decades of research and teaching in operations research, Michael H. Veatch crafted this book to clarify the mathematical underpinnings of optimization. You’ll learn how problem structure drives algorithm efficiency, with a detailed focus on convex optimization and linear programming that connects theory to applications like supply chain management and disaster response. For example, the book doesn’t just list algorithms; it explains their geometric intuition and what makes certain problems solvable in practice. This makes it especially useful if you’re an upper-level math student or someone in economics or computer science looking to deepen your understanding of optimization beyond surface-level methods.

Saul I. Gass's decades of experience in operations research led to this approachable guide that demystifies linear programming without heavy technical jargon. You learn foundational concepts like geometric interpretations and problem-solving techniques, supported by clear examples and an appendix with precise definitions and computational methods. This book suits anyone comfortable with high-school algebra who wants to grasp how linear programming fits within operations research, including network problem applications. If you're looking to build practical intuition rather than dive deep into advanced math, this book offers a solid stepping stone.

This tailored book offers a focused exploration of linear programming techniques, crafted to match your background and learning goals. It reveals core concepts, algorithmic approaches, and practical coding examples that bring optimization methods to life. By customizing the content to your interests and skill level, the book provides a clear pathway through complex topics such as simplex algorithms, duality, and constraint modeling. This personalized guide helps you develop a deep understanding of linear programming’s computational aspects and equips you with the skills to apply these techniques effectively. The tailored approach ensures you engage with the material most relevant to your objectives, accelerating your mastery and confidence.

David C. Vella’s extensive experience teaching college mathematics shines through in this approachable introduction to linear programming and game theory. You’ll find the material laid out in a conversational style that requires only high school algebra, making complex concepts accessible without oversimplifying. The book guides you through graphical methods for linear optimization and offers a fresh proof of the minimax theorem for zero-sum games, alongside explorations of variable-sum and ordinal games. Its progression from motivating examples to more intricate problems encourages creative thinking, making it suited for students in business, economics, and social sciences eager to see how mathematical theory applies to real-world strategic decisions.

Craig A. Tovey challenges the conventional approach to linear programming by integrating duality right from the start, rather than treating it as an afterthought. You’ll find duality woven through the entire book, starting with a clear, general definition in Chapter 1 and continuing with practical examples like the diet problem and zero-sum games. This makes complex topics more intuitive, especially for engineering students encountering rigorous mathematics for the first time. The book also offers modeling tips, computational insights, and hundreds of guided questions to help you grasp difficult concepts thoroughly. If you're looking for a linear optimization text that deeply embeds duality and supports less mathematically sophisticated learners, this is a solid choice.

Drawing from his extensive academic and research career, Giuseppe Lancia offers a focused exploration of compact extended formulations in integer linear programming. This book elucidates the theoretical foundations—covering polyhedra, projections, and integer programming—before guiding you through techniques to develop polynomial-sized models without resorting to complex separation or pricing methods. You’ll find richly illustrated examples spanning combinatorial optimization, network design, and computational biology, helping you grasp how these formulations apply across diverse fields. It’s particularly suited for graduate students and professionals aiming to deepen their understanding of advanced ILP modeling techniques and practical optimization challenges.