Decision-Making Support Models

obligatory courses

(in Polish)

Wymagania wstępne

Algebra liniowa, Analiza matematyczna. Wymagania formalne

Oczekiwana jest podstawowa znajomość algebry i analizy oraz aktywna postawa w trakcie zajęć polegających na formułowaniu rozwiązywaniu zadań.

Założenia wstępne

Znajomość podstaw mikroekonomii oraz teorii podejmowania decyzji ekonomicznych i funkcjonowania przedsiębiors

The aim of the course is to familiarize students with optimization and multicriteria methods useful for solving typical decision problems of an economic nature occurring in the enterprise. A review of methods known and used as part of operational research will be carried out. The aim is to convey the ability to choose and construct the right model for a given decision problem. As a result of practical classes, it will be possible to use the right algorithm to solve and, above all, correctly interpret the received solution. The seminar combines lecture and exercise classes. The course includes the use of the "Operational research with computer" software available in the computer lab. Research element: a project made independently, taking into account the issues and methods presented in the classes.

1. Introduction and description of the subject of classes

- decision-making theory,

- making economic decisions,

- optimization, mathematical programming, operational research.

2. Formulating linear decision problems:

- input-output model,

- classic "diet" problem,

- "cutting-out" task,

- classic problem of "production activity",

- a task in whole numbers,

- multi-criteria task,

- classic "transport" issue,

- the "salesman" network task,

- the "maximum flow" network task,

- network task of the "minimal span",

- PERT network task,

- network task of the "critical path".

3. Simplex method as a universal method of solving linear tasks:

- the first acceptable base solution,

- auxiliary variables and artificial variables,

- interpretation of the obtained results,

- degeneration of the base solution.

4. Duality and dual variables:

- symmetrical and asymmetrical pair of dual tasks,

- information content of simplex board,

- interpretation of dual variables,

- dual price.

5. Duality and dual simplex method:

- dual simplex method,

- interpretation of the obtained results,

- Kuhn-Tucker conditions,

- interpretation of the conditions of complementarity,

- determination of solutions from the Dantzig-Orden conditions.

6. Post-optimal analysis:

- change of coefficients of criterion function,

- application of the simplex method,

- changing the right sides of the restrictive conditions,

- application of the dual simplex method,

- task with parameter.

7. Integer programming:

- method of division and restrictions,

- method of cutting,

- binary programming,

- assignment task.

8. Transport task:

- the first acceptable base solution,

- improving the obtained solution,

- interpretation of optimality indicators.

9. Advanced transport task:

- unbalanced task,

- degenerate base solution,

- unacceptable routes,

- cumulated unit cost,

- a two-step task.

10. Network programming:

- elements of graph theory,

- the shortest path,

- maximum flow in the network,

- minimal spanning tree,

- the traveling salesman problem,

- PERT and critical path analysis.

11. Evolutionary algorithms:

- theory of evolution,

- ecological interpretation,

- genetic algorithm.

12. Multi-purpose programming:

- multicriteria (continuous) methods,

- purposeful programming,

- taking into account the decision-maker's preferences.

13. Multi-attribute programming:

- multi-attribute methods (discrete),

- the ELECTRE method,

- PROMETE method.

14/15. Computer classes:

- transport algorithm,

- allocation problem,

- simplex algorithm,

- post-optimal analysis.

- integer programming,

- multicriteria programming,

- selected network problems.

OBLIGATORY

Trzaskalik T., 2003. Wprowadzenie do badań operacyjnych z komputerem. PWE, Warszawa.

Wagner H.M., 1980. Badania operacyjne. PWE, Warszawa.

SUPPLEMENTARY

Chiang A.C., 1994. Podstawy ekonomii matematycznej. PWE, Warszawa.

Gass S.I., 1976. Programowanie liniowe. PWN, Warszawa.

Ignasiak E. (red.), 2001. Badania operacyjne. PWE, Warszawa.

Kolupa M., 1976. Elementarny wykład algebry liniowej dla ekonomistów. PWN, Warszawa.

Kukuła K. (red.), 1996. Badania operacyjne w przykładach i zadaniach. PWN, Warszawa.

Moore J.H., Weatherford L.R., 2001. Decision Modeling with Microsoft® Excel. Prentice Hall, Upper Saddle River.

Nykowski I., 1980. Programowanie liniowe. PWE, Warszawa.

Sikora W. (red.), 2008. Badania operacyjne. PWE, Warszawa.

Taylor III B.W., 2001. Introduction to Management Science. Prentice Hall, Upper Saddle River.

Thaler R.H., Sunstein C.R., 2013. Impuls. Jak podejmować właściwe decyzje dotyczące zdrowia, dobrobytu i szczęścia. Zysk i Ska Wydawnictwo, Warszawa.

A. Knowledge

1. The student knows the basics of linear optimization. He knows the basics of decision making theory and classification of models supporting decision making.

2. The student knows the classic linear tasks of operational research: the problem of "diet", the problem of "production activity", the "transport" problem.

3. The student knows how, based on basic models, an optimization task is formulated to solve a specific decision problem.

4. The student knows what is the characteristics of multi-criteria decision making.

5. The student knows issues belonging to the group of network problems: "traveling salesman", "maximum flow", "minimal span", "PERT", "critical path".

6. The student knows the algorithms solving the problem of linear programming: simplex algorithm, transport algorithm.

7. The student has knowledge about the problem of duality, with particular consideration of the conditions of complementarity and interpretation of the dual variables.

8. The student knows post-optimal analysis and parametric programming. He knows about the methods of studying the impact of changing the conditions of the task on the optimal solution.

9. The student knows what software is helpful in obtaining optimal solutions to complex decision problems.

B. Skills

1. Student is able to associate a specific decision problem with the right optimization model. He can build the appropriate linear programming task and then solve it and interpret the results.

2. The student is able to use the simplex algorithm and the transport algorithm in order to obtain an optimal solution and interpret its properties.

3. The student is able to analyze the obtained solution in terms of its sensitivity to changes in the conditions of the task. Is able to analyze the results obtained from the point of view of their usefulness in the management process (dual prices).

4. The student can use selected computer programs to determine the solution of the linear optimization task.

C. Social competences

1. The student is aware that making economic decisions can be included in a formal framework to improve the quality of results.

2. The student is aware of the fact that mathematical methods and computer tools supporting decision making processes are at his disposal.

3. The student is able to make decisions conducive to success in the field of individual and social entrepreneurship.

KW01, KW02, KW03, KW04, KW05, KU01, KU02, KU03, KU04, KU05, KU06, KU07, KK01, KK02, KK03

Credit based on a self-made project using the selected decision optimization model