Mathematical Programming for Operations Research
Master the art of mathematical modeling and optimization techniques to solve complex real-world problems in operations research.
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Introduction to Operations Research and Linear Programming
Unit 1: Introduction to Operations Research
What is OR?
OR Applications
OR Problem Solving
OR Modeling
Benefits of Using OR
Unit 2: Introduction to Linear Programming
What is LP?
LP Formulation
Graphical Solutions
Special Cases in LP
LP Applications
Unit 3: Simplex Method
Simplex Intro
Setting up the Tableau
Simplex Iteration
Simplex Example
Special Simplex Cases
Unit 4: Duality and Sensitivity Analysis
Duality Intro
Formulating the Dual
Duality Theorems
Sensitivity Analysis
Applying Sensitivity
Integer Programming: Modeling and Solution Techniques
Unit 1: Introduction to Integer Programming
What is IP?
Why Use IP?
IP Model Components
Binary IP Explained
Mixed Integer Program
Unit 2: Formulating Integer Programming Models
Set Covering
Set Partitioning
Traveling Salesman
Facility Location
Job Scheduling
Nonlinear Programming: Concepts and Methods
Unit 1: Introduction to Nonlinear Programming
What is NLP?
NLP Problem Formulation
Types of NLP Problems
Challenges in NLP
Local vs. Global Optima
Unit 2: Unconstrained Nonlinear Programming
Optimality Conditions
Gradient Descent Methods
Newton's Method
Quasi-Newton Methods
Line Search Techniques
Unit 3: Constrained Nonlinear Programming and KKT Conditions
Equality Constraints
Inequality Constraints
KKT Conditions: Intro
Applying KKT Conditions
KKT Limitations
Dynamic Programming: Sequential Decision Making
Unit 1: Introduction to Dynamic Programming
What is DP?
Principle of Optimality
DP Applications
Stages & States
Actions & Rewards
Unit 2: Formulating DP Models
Identify DP Problems
State Space Definition
Decision Variables
Recursive Equations
Boundary Conditions
Software Tools and Real-World Applications
Unit 1: Introduction to Optimization Software
Optimization Software
Gurobi Installation
CPLEX Installation
Open Source Solvers
Software Environments
Unit 2: Inputting Models into Software
LP Model Input
MIP Model Input
Using Modeling Langs
Data Handling
Debugging Model Input
Unit 3: Analyzing Software Output
Solution Status
Objective Value
Variable Values
Sensitivity Analysis
Post-Optimality
Unit 4: Real-World Applications
Supply Chain Apps
Finance Applications
Healthcare Apps
Energy Applications
Logistics Optimization
