Introduction to linear programming, mathematical programming languages (Julia, Python, AMPL), duality, dual simplex algorithm, integer linear programming, unit commitment, dynamic programming, stochastic programming, hydrothermal programming, stochastic capacity expansion
- Teacher: Παντελής Κάπρος
ECTS : 4
Study Load : theory 4, lab 0
Language : el, en
Learning Outcomes : Knowledge & Understanding
1. Explain the fundamental concepts and assumptions of linear programming and mathematical optimization models, including standard and non-standard formulations
2. Describe the theory behind the simplex method, dual simplex algorithm, and phase I procedures, including feasibility and optimality conditions
3. Interpret the concepts of duality, extreme points, extreme rays, in the context of linear optimization
4. Distinguish between linear, integer, and dynamic programming models and their respective solution techniques
Application & Analysis
5. Formulate real-world problems as linear and integer programming models with appropriate objective functions and constraints
6. Apply the simplex and dual simplex algorithms to solve optimization problems, including those not in standard form
7. Analyze feasibility, boundedness, and optimality of solutions using theoretical and computational tools
8. Implement optimization models using Julia or Python-based solvers for practical problem-solving
Evaluation & Synthesis
10. Compare different optimization approaches (linear, integer, dynamic programming) and evaluate their suitability for specific applications
11. Critically assess the efficiency and limitations of solution algorithms in complex optimization scenarios
12. Design and present a complete optimization project, including model formulation, computational implementation, and interpretation of results