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Subjects

1. Decision making and operations research.
1.2. The need for optimization.
1.3. Typical models of industry and finance.
2. Linear programming (LP).
2.1. Need for linear models.
2.2. General form of LP problems.
2.3. Multiobjective optimization, goal programming.
2.4. Economic interpretation of the optimality conditions: Sensitivity analysis.
2.5. The primal simplex (SX) method.
2.6. Duality and the dual simplex method.
2.7. State-of-the-art in solving LP problems.
3. Large scale LP problems.
3.1. Characteristics.
3.2. Data structures.
3.3. MPS format.
3.4. Presolve.
3.5. Scaling.
4. Advanced simplex techniques.
4.1. Product/elimination form of the inverse (PFI/EFI).
4.2. Pricing.
4.3. Handling degeneracy.
4.4. Creating starting bases.
4.5. State-of-the-art in computational SX.
5. Integer programming (IP).
5.1. Situations requiring integer valued models.
5.2. IP problem formulation.
5.3. Solution methods; Implicit enumeration, branch and bound (B&B) method.
5.4. Network programming (optimization in networks).
5.5. Logic constraints and IP.
5.6. State-of-the-art in solving IP problems.
6. Modeling
6.1. Basics of modeling.
6.2. Model generation and management.
6.3. Modeling languages, modeling systems.

Case studies, computer demonstrations where appropriate.