Here’s a list of 100 chapter titles on Operations Research, progressing from beginner to advanced levels, with a focus on mathematical aspects:
- Introduction to Operations Research: Mathematical Foundations
- The Role of Operations Research in Decision Making
- Mathematical Modeling in Operations Research
- Linear Algebra for Operations Research
- Basic Concepts in Optimization: A Mathematical Overview
- Problem Formulation and Structure in Operations Research
- The Simplex Method: Introduction and Basic Concepts
- Introduction to Linear Programming: Formulation and Solving
- Graph Theory Basics: An Essential Tool for Operations Research
- The Transportation Problem: Formulation and Solution Methods
- The Assignment Problem: Solving with Linear Programming
- Integer Programming: Integer Variables in Optimization Models
- Sensitivity Analysis: Understanding the Impact of Parameter Changes
- Duality Theory: Concepts and Applications in Linear Programming
- The Simplex Algorithm: Step-by-Step Solution Procedure
- The Dual Simplex Method: An Extension of the Simplex Algorithm
- Introduction to the Hungarian Method for the Assignment Problem
- The Transportation Simplex Method: Solving Transportation Problems
- Basic Probability Concepts for Operations Research
- Introduction to Queueing Theory and Its Applications
- The Duality Theorem and Its Role in Optimization Problems
- The Fundamental Theorem of Linear Programming
- Convex Sets and Convex Functions in Optimization
- The Karmarkar Algorithm: A New Approach to Linear Programming
- The Revised Simplex Method: Computational Efficiency
- Nonlinear Programming: Introduction to Nonlinear Optimization
- The Karush-Kuhn-Tucker Conditions for Constrained Optimization
- The Maximum Flow Problem and Ford-Fulkerson Algorithm
- Network Flow Models: Applications in Operations Research
- Integer Linear Programming: Branch and Bound Method
- Cutting Plane Methods: Approaches for Solving Integer Programs
- Dynamic Programming: Multistage Decision Making
- The Bellman Equation: Recursion in Dynamic Programming
- Deterministic Dynamic Programming: A Step-by-Step Approach
- Inventory Management: Mathematical Models and Techniques
- The Economic Lot Scheduling Problem: Optimization in Production
- Markov Chains and Their Application to Decision Processes
- The Traveling Salesman Problem: Mathematical Formulation and Solution Methods
- The Vehicle Routing Problem: Optimization in Logistics
- Game Theory: Basic Concepts and Applications in Operations Research
- Network Optimization Problems: Flow, Cuts, and Shortest Paths
- The Simplex Method in High Dimensions: Computational Techniques
- Interior Point Methods: A New Paradigm for Linear Programming
- Benders Decomposition: A Strategy for Large-Scale Optimization
- Stochastic Programming: Optimization under Uncertainty
- Convex Optimization: Theory and Algorithms
- Advanced Topics in Nonlinear Optimization: Local and Global Methods
- Linear Matrix Inequalities in Optimization Problems
- Optimal Control Theory: Mathematical Formulation and Applications
- The Dynamic Lot Sizing Problem: Models and Algorithms
- The Lagrangian Relaxation Method in Integer Programming
- The Master Theorem for Integer Programming
- The Geometry of Integer Programming: Convex Hulls and Cutting Planes
- Robust Optimization: Solving Problems under Uncertainty
- Semi-Definite Programming: Theory and Applications
- Stochastic Processes: Models for Random Systems in Operations Research
- Markov Decision Processes: Theory and Applications
- Queueing Systems: Advanced Mathematical Models and Techniques
- Multi-Objective Optimization: Mathematical Framework and Solution Methods
- Heuristic Methods in Operations Research: Overview and Applications
- Genetic Algorithms in Optimization Problems
- Simulated Annealing: A Probabilistic Approach to Optimization
- Ant Colony Optimization: Swarm Intelligence in Operations Research
- The Use of Monte Carlo Simulation in Operations Research
- Simulation Optimization: Combining Simulation and Optimization Methods
- Metaheuristics: Methods for Solving Complex Optimization Problems
- Large-Scale Optimization: Techniques for Solving Big Problems
- The Theory of Stochastic Processes in Operations Research
- Game Theory and Its Applications in Network Optimization
- Linear Programming Duality: Theoretical and Computational Insights
- The Lagrange Multiplier Method in Constrained Optimization
- The Ellipsoid Algorithm: Solving Linear Programming Problems
- Decomposition Techniques in Large-Scale Optimization
- The Knapsack Problem: Formulation and Solution Approaches
- The Maximum Flow/Minimum Cut Theorem: Theory and Applications
- Integer Programming with Mixed Integer Variables: Solving Methods
- The Cutting Stock Problem: Optimization in Manufacturing
- Multi-Stage Stochastic Programming: Models and Applications
- The Newsvendor Problem: Inventory Optimization under Uncertainty
- The Financial Portfolio Optimization Problem: Risk and Return
- Advanced Integer Programming: Branch-and-Cut Algorithms
- Nonlinear Programming and Global Optimization: Advanced Methods
- Optimal Scheduling in Complex Systems: Algorithms and Models
- The Traveling Salesman Problem in Higher Dimensions
- Large-Scale Network Design Problems in Operations Research
- Game Theory and Nash Equilibrium in Network Optimization
- Decomposition Algorithms for Solving Large-Scale Linear Programs
- The Theory of Semi-Definite Programming in Optimization
- Cooperative Game Theory and Its Applications in Operations Research
- Deep Learning and Operations Research: New Mathematical Insights
- Integer Linear Programming with Nonlinear Constraints
- Robust and Stochastic Optimization: Dual Algorithms and Techniques
- Advanced Queueing Theory: From Simple Models to Complex Systems
- Optimal Transport Problems: Mathematical Formulations and Algorithms
- Mixed-Integer Nonlinear Programming: Approaches and Techniques
- The Theory of Bilevel Programming: Optimization under Hierarchical Structures
- Mathematical Programming Models for Supply Chain Optimization
- The Theory of Evolutionary Game Theory in Operations Research
- The Application of Convex Analysis in Optimization Problems
- Advanced Computational Techniques for Solving Large-Scale Problems
These chapters cover the full range of topics within operations research, from fundamental concepts and linear programming to advanced methods, algorithms, and applications in various domains. The topics combine theoretical foundations with practical problem-solving techniques, ensuring a solid understanding of both the mathematical and computational aspects of the field.