OPTIMUM PROGRAMMING
Syllabus of the course

1. Optimization models and methods
   
   
   1. Optimization problems and their reprezentation by mathematical models
   2. Stages of model design
   3. Methods for models solving
   
   
2. Methods for models solving (LP)
   
   
   1. Description of linear programming problem and its mathematical formulation
      
   2. Simplex method. Primal algorithm derivation. Simplex tableau.
      
   3. Duality in linear programming.
      
   4. Interpretation of LP problem solution
      
   5. Sensitivity analysis and stability of LP problem solution
      
   
   
3. Linear programming - distribution problems
   
   
   1. Mathematic formulation of a transportation problem. Unbalanced transportation problems. Methods for finding basic feasible solution. Methods for finding optimum solution
      
   2. Sensitivity analysis for transportation problems
      
   3. Assignment problem
      
   
   
4. Nonlinear programing (NLP)
   
   
   1. General NLP problem. Mathematical formulation of NLP
      
   2. Unconstrained and constrained problem . Lagrange function. Kuhn-Tucker conditions
      
   3. Quadratic programming problem. Wolfe method for solving quadratic programming problems
      
   
   
5. Network analysis (NA)
   
   
   1. Basic terms and definitions of graph theory
      
   2. CPM-PERT project scheduling models
      
   3. Crashing the project analysis
      
   4. Shortest path problems
      
   5. Maximum flow problems
      
   6. Minimum spanning tree problems
   
   
6. Input-output analysis
   
   
   1. Description of input-output models
      
   2. System of distribution and cost equations
      
   3. Calculation based on distribution and cost equations