Operations Research Methods

Syllabus

• Linear programming fundamentals and the geometry of feasible solution sets.
• The simplex method and its interpretation in solving linear programming problems.
• The dual simplex method and its applications.
• Farkas' lemma, linear programming duality and the strong duality theorem.
• The connection between absence of arbitrage and risk-neutral measures, with proof based on strong duality.
• Mixed-integer linear programming and the branch-and-bound method.
• Cutting-plane methods for integer and mixed-integer optimization.
• Bank cash optimization as an applied operations research problem.
• Portfolio optimization and financial applications of mathematical programming.
• Data analysis problems formulated as linear and mixed-integer programming models: regression, clustering and classification.