May 1, 2024
Updated May 9, 2025
20 minute read
Linear Programming (LP) is a mathematical method used to find the best possible outcome in a given situation where the requirements and objectives can be expressed as linear relationships. Think of it as a systematic way to make optimal decisions when faced with limitations or constraints. It's a powerful tool for optimizing resources, whether that means maximizing profit, minimizing cost, or achieving the most efficient allocation. For those new to the concept, imagine you have a set of ingredients (resources) and you want to bake cakes (products) in a way that earns you the most money (objective), given that each cake requires a specific amount of each ingredient and you only have a limited supply of those ingredients. Linear programming helps you figure out the ideal number of each type of cake to bake.
Working with linear programming can be quite engaging. It allows individuals to tackle complex real-world problems by translating them into a structured mathematical framework. This process of modeling and solving can be intellectually stimulating, offering a blend of analytical thinking and practical application. Furthermore, the impact of finding an optimal solution can be significant, leading to substantial improvements in efficiency and decision-making across various fields. The ability to quantify problems and derive clear, actionable solutions is a key aspect that many find exciting and rewarding.
What is Linear Programming?
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Reading list
We've selected 29 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Linear Programming.
Provides a comprehensive introduction to linear optimization, covering both theory and algorithms. It is suitable for both undergraduate and graduate students.
Is considered a modern standard for graduate-level courses in linear programming, offering a deep understanding of the subject. It is particularly strong in theory and is widely used as a textbook in academic institutions. While comprehensive, it assumes a certain level of mathematical maturity.
Considered a classic in the field, this book provides a rigorous and in-depth treatment of the theory of linear and integer programming. It is aimed at graduate students and researchers and is more focused on theoretical aspects and algorithms with a focus on complexity analysis.
Provides a solid theoretical foundation in linear programming and covers important extensions. It is suitable for advanced undergraduates and graduate students. The book is known for its clear explanations and is used in graduate-level courses.
A classic and comprehensive text covering the fundamental ideas and principles of linear programming. It is well-regarded for its clear proofs and is suitable for graduate courses in operations research, mathematics, and computer science. While older, it remains a valuable resource for its theoretical depth.
While focused on integer programming, this book builds upon a solid understanding of linear programming and delves into advanced topics and recent developments in integer and mixed-integer programming. It is suitable for graduate students and researchers interested in this important extension of linear programming.
This comprehensive book covers both linear programming and network flows, highlighting the close relationship between these two areas. It is often used for graduate-level courses and provides a thorough treatment of theoretical and algorithmic aspects.
Takes a modern approach by introducing duality early and integrating it throughout the text. It aims to help students develop a strong understanding of duality theory and is suitable for advanced undergraduate and graduate students.
Offers a good introduction to the geometry, simplex method, duality, and interior point methods in linear programming, with proofs. It is suitable for students looking for a solid theoretical foundation with clear explanations. It can be a good supplementary text for undergraduate and graduate courses.
Focuses on the crucial aspect of formulating real-world problems as mathematical programming models, including linear programming. It is highly practical and valuable for students and professionals who need to apply linear programming to solve actual problems. It complements theoretical texts by focusing on the modeling process.
Classic text on linear programming in operations research. It is suitable for both undergraduate and graduate students.
Classic introductory text on linear programming, known for its clear and comprehensive coverage of techniques. It introduces theoretical, computational, and applied aspects and is suitable for undergraduates. It's a foundational book that has been used for many years.
Offers an in-depth look at both simplex-based and interior point methods for solving linear programming problems. It provides a strong theoretical foundation and covers computational aspects, making it suitable for students and professionals in various quantitative fields.
Offers a different approach to linear programming, focusing on algorithm design and the structure of linear programs before introducing the simplex method. It provides good coverage of modeling and is suitable for a solid understanding of the underlying principles.
This recent publication (2021) provides information needed to understand various simplex methods and other techniques for solving linear programming problems. It includes practical examples and discusses multi-criteria decision-making methods. is useful for professors and students interested in contemporary approaches and applications.
While focused on integer programming, this book is highly relevant for those interested in applying optimization techniques to real-world problems. It covers modeling and solution methods for integer programming, which often follows from a foundation in linear programming. It's a valuable resource for practitioners and advanced students.
Covers combinatorial optimization with a strong emphasis on algorithms and complexity, where linear programming plays a significant role, particularly in areas like network flows and duality. It's suitable for advanced undergraduates and graduate students in computer science and operations research.
Covers both linear and nonlinear optimization, providing a broader perspective on optimization techniques. The linear programming sections are comprehensive and suitable for students looking for a text that bridges the gap between linear and nonlinear methods.
Classic text on linear programming and economic analysis. It is suitable for graduate students and researchers in economics.
Intended for a first course in linear programming at the undergraduate level, this book emphasizes linear programming skills through algorithmic solutions of small-scale problems and their applications. It is designed to be accessible and addresses common difficulties faced by students.
Offers a good introduction to the basic theory and computation in linear programming, with a focus on finite improvement algorithms. It includes material on mathematical proof techniques and is suitable for students looking to understand the algorithmic aspects.
This text is oriented towards introducing important ideas in linear programming at a fundamental level, focusing on applications to managerial problems. It is written for students and executives with no previous background in linear programming and avoids complex mathematical derivations. This good resource for those seeking a practical, less theoretical introduction.
Provides a comprehensive treatment of nonlinear programming. It is suitable for graduate students and researchers.
For more information about how these books relate to this course, visit:
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