*Conducted in terms:*2019L, 2020L

*Erasmus code:*14.3

*ISCED code:*0311

*ECTS credits:*3

*Language:*Polish

*Organized by:*Faculty of Economic Sciences

*Related to study programmes:*

# Advanced decision optimization models 2400-IiE3ZMOD1

1/2. Linear programming (advanced)

- sensitivity analysis of the optimal solution

- dual simplex method

- post-optimal analysis of criterion function coefficients

- post-optimal analysis of the words of the right parties

- parametric programming

3/4. Integer programming

- branch and bound method

- Gomory method

- binary programming

- assignment model

5/6. Advanced transportation model

- unbalanced task

- degenerate base solution

- unacceptable routes

- cumulated unit cost

- a two-step task

7/8. Network programming

- elements of graph theory

- the shortest path

- maximum flow in the network

- minimal spanning tree

- traveling salesman problem

- PERT and critical path analysis

9/10. Convex programming

- Kuhn-Tucker conditions

- interpretation of Lagrange multipliers

- economic applications

- square programming

11/12. Multicriteria programming

- multicriteria (continuous) methods

- multi-attribute methods (discrete)

- goal programming

- taking into account the decision-maker's preferences

- ELECTRE

13/14. Dynamic and stochastic programming

- dynamic programming model

- stochastic programming model

- economic applications

- genetic and evolutionary algorithms

15. 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.

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.

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.

KW01, KW02, KW03, KU01, KU02, KW03, KK01, KK02, KK03

## Assessment criteria

Credit based on the assessment of a self-written project (construction, solution and interpretation of the model result), and requiring using a computer program

## 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

Information on *level* of this course, *year of study* and semester when the course
unit is delivered, types and amount of *class hours* - can be found in course structure
diagrams of apropriate study programmes. This course is related to
the following study programmes:

Additional information (*registration* calendar, class conductors,
*localization and schedules* of classes), might be available in the USOSweb system: