Here are 100 chapter titles for a comprehensive study of Operations Research methods, progressing from beginner to advanced levels:
I. Introduction & Linear Programming (1-20)
- Introduction to Operations Research: History and Scope
- The OR Approach: Problem Formulation and Model Building
- Linear Programming: Introduction and Formulation
- Graphical Solution of Linear Programming Problems
- The Simplex Method: Maximization Problems
- The Simplex Method: Minimization Problems
- The Big M Method and Two-Phase Method
- Special Cases in Simplex: Degeneracy, Unboundedness, Infeasibility
- Duality in Linear Programming: Primal and Dual Problems
- The Dual Simplex Method
- Sensitivity Analysis and Post-Optimality Analysis
- Applications of Linear Programming: Real-World Examples
- Linear Programming Software and Tools
- Introduction to Modeling Languages (e.g., AMPL, GAMS)
- Integer Programming: Introduction and Formulations
- Cutting Plane Methods for Integer Programming
- Branch and Bound Method for Integer Programming
- 0-1 Integer Programming and Binary Variables
- Applications of Integer Programming
- Practice Problems: Linear Programming
II. Transportation & Network Optimization (21-40)
- The Transportation Problem: Formulation and Solution
- The Transportation Simplex Method
- Variations of the Transportation Problem
- The Assignment Problem: Formulation and Solution
- The Hungarian Method
- Transshipment Problems
- Network Optimization: Introduction and Terminology
- Shortest Path Algorithms: Dijkstra's Algorithm
- Shortest Path Algorithms: Bellman-Ford Algorithm
- Maximum Flow Problems: Ford-Fulkerson Algorithm
- Max-Flow Min-Cut Theorem
- Minimum Cost Flow Problems
- Network Simplex Method
- Project Management: CPM and PERT
- Critical Path Analysis
- Time-Cost Trade-Offs in Project Management
- Resource Allocation in Project Management
- Applications: Network Optimization in Supply Chain
- Applications: Project Management in Construction
- Practice Problems: Transportation and Network Optimization
III. Nonlinear Programming & Optimization (41-60)
- Nonlinear Programming: Introduction and Formulations
- Unconstrained Optimization: Necessary and Sufficient Conditions
- Gradient-Based Optimization Methods: Steepest Descent
- Conjugate Gradient Methods
- Newton's Method and Quasi-Newton Methods
- Constrained Optimization: Lagrange Multipliers
- Karush-Kuhn-Tucker (KKT) Conditions
- Quadratic Programming: Introduction and Solution Methods
- Separable Programming
- Geometric Programming
- Dynamic Programming: Introduction and Principles
- The Principle of Optimality
- Dynamic Programming: Applications to Resource Allocation
- Dynamic Programming: Applications to Inventory Control
- Stochastic Dynamic Programming
- Applications: Nonlinear Optimization in Engineering
- Applications: Dynamic Programming in Finance
- Introduction to Metaheuristics: Genetic Algorithms
- Simulated Annealing
- Tabu Search
IV. Inventory & Queuing Theory (61-80)
- Inventory Management: Introduction and Models
- Economic Order Quantity (EOQ) Model
- Production Lot Size Model
- Inventory Models with Shortages
- Inventory Models with Uncertain Demand
- Safety Stock and Service Level
- Multi-Item Inventory Models
- Inventory Control Systems: Periodic and Continuous Review
- Applications: Inventory Management in Retail
- Queuing Theory: Introduction and Terminology
- Basic Queuing Models: M/M/1, M/M/c
- Queuing Models with Finite Capacity
- Queuing Models with Impatient Customers
- Priority Queuing Models
- Queuing Networks: Jackson Networks
- Applications: Queuing Theory in Call Centers
- Applications: Queuing Theory in Healthcare
- Simulation: Introduction and Principles
- Discrete-Event Simulation
- Simulation Languages and Software
V. Advanced Topics & Decision Analysis (81-100)
- Game Theory: Introduction and Basic Concepts
- Two-Person Zero-Sum Games
- Non-Zero-Sum Games
- Game Theory: Applications in Business
- Decision Theory: Decision Making under Uncertainty
- Decision Trees and Decision Analysis
- Bayesian Decision Theory
- Markov Decision Processes (MDPs)
- Applications: Decision Analysis in Finance
- Applications: Game Theory in Economics
- Stochastic Programming: Introduction and Methods
- Robust Optimization
- Goal Programming
- Multi-Objective Optimization
- Heuristics and Metaheuristics: Advanced Topics
- Constraint Programming
- Operations Research in Service Industries
- Operations Research in Healthcare
- Operations Research in Supply Chain Management
- The Future of Operations Research and Analytics