Advanced decision optimization models 2400-IiE3ZMOD1
1. Linear programming (advanced)
- simplex method
- sensitivity analysis of the optimal solution
- post-optimal analysis of criterion function coefficients
- post-optimal analysis of the right hand side coefficients
- parametric programming
2. Dual problem
- construction of dual task
- interpretation of dual task
- optimal solution of dual task
- dual variables and their interpretation
3. Integer programming
- branch and bound method
- Gomory method
- binary programming
- assignment model
4. Transportation model advanced
- unbalanced task
- degenerate base solution
- unacceptable routes
- cumulated unit cost
- a two-step task
5. Network programming
- elements of graph theory
- the shortest path
- maximum flow in the network
- minimal spanning tree
- traveling salesman problem
- genetic algorithm
6. CPM and PERT
- critical path method analysis
- project management
- time vs. cost analysis
7. Multicriteria programming
- multicriteria (continuous) methods
- multi-attribute methods (discrete)
- goal programming
- taking into account the decision-maker's preferences
- AHP, PROMETHEE, ELECTRE
8. Dynamic and stochastic programming
- dynamic programming model
- stochastic programming model
- economic applications
9. Discussion of students' projects
Type of course
Prerequisites (description)
Course coordinators
Learning outcomes
A. Knowledge
1. The student knows and understands the simplex method, sensitivity analysis of the optimal solution, the dual simplex method, parametric programming.
2. The student knows integer programming in the form of a division method and constraints as well as the method of cutting. He knows the principles of formulating a task with binary variables.
3. The student knows the transport task in the basic and advanced form removing the limiting assumptions of the basic model.
4. The student has knowledge about network programming, taking into account typical tasks: the shortest path, the maximum flow in the network, the minimum spanning tree, the traveling salesman problem.
5. The student knows and understands project management in a model approach using PERT analysis and critical path analysis.
6. The student knows the multicriteria problem, and in particular the methods of solving it: AHP, Electre, Promethee.
7. The student knows dynamic and stochastic programming. Has knowledge of the functioning and use of the genetic and evolutionary algorithm.
(S2A_W06; S2A_W07; S2A_W08; S2A_W11)
B. Skills
1. The student can properly recognize the type of decision problem, make its mathematical formalization and choose the appropriate model leading to the optimal solution.
2. The student has the ability to use computerized operational research programs and mathematical programming to solve complex decision problems.
3. The student can correctly interpret the obtained optimal solution and perform a post-optimal analysis of its suitability.
(S2A_U01; S2A_U02; S2A_U06; S2A_U07)
C. Social competences
1. The student is aware that even complex decision problems in the field of broadly understood management can be solved with the use of mathematical methods and computer technology.
2. The student is able to use the acquired knowledge to improve the quality of decisions made, in the field of individual and social entrepreneurship.
(S2A_K03; S2A_K04; S2A_K05; S2A_K07)
Assessment criteria
Assessment based on a self-prepared project requiring the construction, solution and interpretation of the model result, and at the same time the use of a computer program. In addition, attendance at classes, homework and written control papers will be checked.
Bibliography
Obligatory
Sikora W. (red.), 2008. Badania operacyjne. PWE, Warszawa.
Trzaskalik T., 2003. Wprowadzenie do badań operacyjnych z komputerem. PWE, Warszawa.
Supplementary
Chiang A.C., 1994. Podstawy ekonomii matematycznej. PWE, Warszawa.
Galas Z., Nykowski I., Żółkiewski Z., 1987. Programowanie wielokryterialne. PWE, Warszawa.
Grabowski W., 1980. Programowanie matematyczne. PWE, Warszawa.
Ignasiak E. (red.), 2001. Badania operacyjne. PWE, Warszawa.
Moore J.H., Weatherford L.R., 2001. Decision Modeling with Microsoft® Excel. Prentice Hall, Upper Saddle River.
Taylor III B.W., 2001. Introduction to Management Science. Prentice Hall, Upper Saddle River.
Wagner H.M., 1980. Badania operacyjne. PWE, Warszawa.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: