Top 7 Books on Linear Programming
Linear programming is a set of mathematical and computational tools used in mathematical programming. It helps to solve systems of linear equations and inequalities while maximizing or minimizing some linear function. It's used for obtaining the most optimal solution for a problem with given constraints.
Are you looking for the best linear programming books? This post will talk about some must-read Linear programming books that suit your requirements.
Linear “programming” is not related to computer programming, although studying linear programming is often a requirement in a computer science major. This type of mathematical problem solving can be extremely valuable in a computer science-related profession.
Why Learn Linear Programming?
Linear programming is a fundamental optimization technique that’s precise, fast, and suitable for a range of practical applications. It is a versatile technique that can be used to represent several real-world situations.
Easier to learn: The beauty of Linear programming is its incredible simplicity and easy way of understanding.
Improves quality of decisions: Linear programming techniques improve the quality of decisions. The decision-making approach of the user of this technique becomes more objective and less subjective.
Flexible: It gives you a lot more flexibility and helps to solve a wide range of problems.
Solve complex problems: It helps to solve many diverse combination problems. It can solve problems that involve multiple variables and constraints.
Widely used: Linear programming is widely used in management, research science, and business.
What Makes Best Linear Programming Books?
Here are our criteria for the selection of the books:
A linear programming book should contain a variety of instructional materials, including exercises, examples, questions, learning activities, and other features that promote a programmer’s engagement and active learning.
It must have a structured, clear, and logical progression of topics.
Content must be up-to-date and should thoroughly teach and explain the basic concepts of Linear programming
Use clear, precise, and easy-to-understand language.
Linear programming books should have a clear layout. It must be friendly toward self-taught programmers.
Best Books on Linear Programming
Although there are many online resources, learning from books is still one of the best ways to master Linear programming.
Here are the five best books to learn Linear programming:
1. Best Book for Beginners: Linear Programming: An Introduction to Finite Improvement Algorithms
Linear Programming: An Introduction to Finite Improvement Algorithms by Daniel Solow covers the basic theory and computation in linear programming. It has substantial material on mathematical proof techniques and sophisticated computation methods.
The book is divided into eleven chapters and the contents include:
Chapter 1 talks about Problem Formulation
Chapter 2 covers Geometric Motivation
Chapter 3 talks about Proof Techniques
Chapter 4 covers Linear Algebra
Chapter 5 talks about the Simplex Algorithm
Chapter 6 talks about Phase 1 problems
Chapter 7 covers Computational Implementation
Chapter 8 covers Duality Theory
Chapter 9 covers Sensitivity and Parametric Analysis
Chapter 10 covers Techniques for Handling Bound Constraints
Chapter 11 talks about Network Flow Problems
The useful appendixes explain how to use Excel to solve linear programming problems. The book is written in a very clear and easy-to-grasp style. It also includes numerous examples and exercises.
2. Best Book for Hands-on Learners: Linear Programming: Methods and Applications
Linear Programming: Methods and Applications by Dr. Saul I. Gass introduces theoretical, computational, and applied concepts of linear programming. It gives a clear and comprehensive coverage of the entire spectrum of linear programming techniques.
The theoretical and computational methods discussed in the book include:
The general linear programming problem
The simplex computational procedure
The revised simplex method
The duality problems of linear programming
Parametric linear programming
Additional computational techniques
The book also covers transportation problems and general linear programming applications. There are numerical examples and exercises with every chapter. If you are looking for a fun and approachable book for Linear Programming, then this book is for you.
3. Best Book for Serious Learners: Linear Programming, Vasek Chvátal
Linear Programming by Vasek Chvatal covers basic theory, selected applications, network flow problems, and advanced techniques.
As you go through the book, you will learn:
Specific examples to illuminate practical and theoretical aspects of the subject
The structures of fully detailed proofs
Modern efficient implementations of the simplex method
Appropriate data structures for network flow problems.
This book is completely self-contained. It develops even elementary facts on linear equations and matrices from the beginning. This book is a fun read and valuable to have on your shelf!
4. Best Book for Advanced Programmers: Linear Programming
Linear Programming, 5th edition by Vanderbei provides a broad introduction to both the theory and the application of optimization. It gives a special emphasis on the elegance, importance, and usefulness of the parametric self-dual simplex method.
The book is divided into 25 chapters and the contents covered are:
Chapter 1 gives you the Introduction
Chapter 2 talks about the Simplex Method
Chapter 3 covers Degeneracy
Chapter 4 talks about the Efficiency of the Simplex Method
Chapter 5 covers Duality Theory
Chapter 6 covers the Simplex Method in Matrix Notational
Chapter 7 covers Sensitivity and Parametric Analyses
Chapter 8 talks about Implementation Issues
Chapter 9 covers Problems in General Form
Chapter 10 talks about Convex Analysis
Chapter 11 covers Game Theory
Chapter 12 talks about Data Science Applications
Chapter 13 talks about Financial Applications
Chapter 14 covers Network Flow Problems
Chapter 15 covers Applications
Chapter 16 covers Structural Optimization
Chapter 17 talks about the Central Path
Chapter 18 covers Path-Following Method
Chapter 19 covers the KKT System.
Chapter 20 talks about the Implementation Issues
Chapter 21 talks about the Affine-Scaling Method
Chapter 22 covers the Homogeneous Self-Dual Method
Chapter 23 covers Integer Programming
Chapter 24 covers Quadratic Programming
Chapter 25 covers Convex Programming.
This latest edition also includes a discussion of modern Machine Learning applications, a section explaining Gomory Cuts, and an application of integer programming to solve Sudoku problems.
The contents of this book are concise and well-constructed. All the topics are clearly developed with many numerical examples worked out in detail.
5. Best Book for Visual Learners: Linear Programming and Resource Allocation Modeling
Linear Programming and Resource Allocation Modeling by Michael J. Panik guides you in the application of linear programming to firm decision making. The book provides a complete treatment of linear programming as applied to activity selection and usage.
The book is divided into 14 chapters. These chapters in the book cover the following:
Chapter 1 gives you the introduction
Chapter 2 covers Mathematical Foundations
Chapter 3 gives an introduction to Linear Programming
Chapter 4 covers Computational Aspects of Linear Programming
Chapter 5 covers Variations of the Standard Simplex Routine
Chapter 6 talks about duality theory
Chapter 7 covers Linear Programming and the Theory of the Firm
Chapter 8 covers Sensitivity Analysis
Chapter 9 talks about Analyzing Structural Changes
Chapter 10 covers Parametric Programming
Chapter 11 talks about Parametric Programming and the Theory of the Firm
Chapter 12 again discusses Duality
Chapter 13 covers Simplex‐Based Methods of Optimization
Chapter 14 covers Data Envelopment Analysis (DEA)
The book includes many detailed example problems as well as textual and graphical explanations. The contents will make you stay focused and you will not be bored!
6. Best Book for Researchers: Introduction to Mathematical Optimization by Matteo Fischetti
Introduction to Mathematical Optimization by Matteo Fischetti will let you learn Linear Programming with an exposition of the most recent resolution techniques, and in particular of the branch-and-cut method.
This book is intended for students in Operations Research and Mathematical Optimization for scientific faculties. Some of the basic topics of Operations Research and Optimization are considered:
Integer Linear Programming
All the contents are well organized. This book is filled with practical information, numerous examples, and exercises. This book will simply polish your Linear Programming skills from good to outstanding!
7. Best Book for Completionists: Optimization Using Linear Programming
Optimization Using Linear Programming by A. J. Metei and Veena Jain emphasize the solution of various types of linear programming problems. This is done using different kinds of software including MS-Excel, solutions of LPPs by Mathematica, MATLAB, WinQSB, and LINDO.
The book includes numerous application examples and exercises. It also includes the necessary definitions and theorems to master theoretical aspects.
The book is divided into 9 chapters and the contents covered are:
Chapter 1 covers the basics of linear algebra using MS Excel
Chapter 2 introduces the reader to LLP's and the graphical method
Chapter 3 talks about simplex method-1
Chapter 4 talks about simplex method-2
Chapter 5 covers duality
Chapter 6 covers sensitivity analysis
Chapter 7 talks about transportation and transshipment problems
Chapter 8 covers assignment problems
Chapter 9 talks about game theory
This book is for engineers, mathematicians, computer scientists, financial analysts, and anyone interested in learning linear programming.
More Ways to Learn Linear Programming
That wraps our article about some of the best books to learn linear programming. It is hard to say which is the best book as it depends upon your background and choice.
You now know what linear programming is and what are some of the best books to learn it. We hope our book curation will help you to pick the right book to learn linear programming. These books will make your journey of learning linear programming a smooth one.
If you are not really into books, you can check out a plethora of online learning resources that are available:
Udemy: Linear Programming for Optimization by Girijesh Pathak is an inexpensive course cheaper than a textbook over 80 5-star reviews and over 6 hours of video content. The course teaches you to build a strong foundation of optimization techniques.
RealPython: Hands-On Linear Programming: Optimization With Python by Mirko Stojiljković. In this free tutorial, you learn what linear programming is and how to solve linear programming problems with Python.
Coursera: Coursera offers some great linear programming courses. These high-rated courses will help you learn the concepts of linear programming.
If you are studying linear programming as a result of learning computer science, you maybe interested in the over 70 free coding resources we have gathered. Good luck with your mathematic adventures and I hope to see you in another article.