🔄 Optimization

The subtopic Optimization contains materials and calculation tools for the following optimization problems:

-Simplex method

-Integer programming

-Multi-objective optimization (Pareto optimal)

-Nonlinear optimization

-Transport optimization

The Documents & Materials area contains a mathematical description of each calculation tool and tasks (2 tasks each for 3 levels of difficulty).

The following elements are discussed in detail:

Simplex method

-The general linear program

-Geometric interpretation (2 variables)

-The simplex algorithm

-Duality

-Shadow prices

-Dual simplex algorithm

Integer programming

-Types of integer programs

-The Branch & Bound Algorithm

-Special structures: binary programs

Multi-objective optimization (Pareto optimum)

-The general multi-objective optimization problem

-Solution methods

-Pareto front: graphical representation

-Decision support: choosing a solution

Nonlinear optimization

-The general nonlinear problem

-Gradient and Hessian matrix

-Gradient method

-Newton method

-Contour plot - visualization of the objective function

Transportation optimization

-The transport problem

-Starting solution: Northwest corner method

-Starting solution: Minimum cost method

-Starting solution: Vogel approximation (VAM)

-Optimization: MODI method

-Extensive example