Linear Optimization
- Introduction to linear programming, modeling of some simple examples
- Model building (Work-Scheduling problem, Blending Problem, Cutting stock problem, Project selection problem)
- Model building (Production planning problem, Multi-period decision problem, Multi-period financial problem); pyomo package in python to solve optimization models
- Graphical solutions of LPs, Special cases (Alternative optimal solutions, Infeasibility, Unboundedness, Degeneracy), Redundant, binding and non-binding constraints
- Basic feasible solutions; Representation theorem; Relation between extreme points and basic feasible solutions; Simplex Algorithm
- Considering special cases in Simplex method (Unboundedness, Degeneracy, Alternative optimal solutions)
- Big M method; Two-phase Simplex method
- Advanced topics (Methods to resolve cycling, Interior point method)
- Revised Simplex method,
- Primal and Dual problems, Formulation of Dual problem, Dual theorems
- Economic interpretation of the dual problem, Shadow price, Dual Simplex method,
- Sensitivity Analysis
- Parametric programming, Economic Interpretation based on the solver output
- Simplex method for the transportation problem
- Simplex method for the transportation problem