OPF:INMBAOAN Operational Analysis for Econo - Course Information

INMBAOAN Operational Analysis for Economists

Extent and Intensity

2/1/0. 4 credit(s). Type of Completion: zk (examination).

Teacher(s)

Ing. Elena Mielcová, Ph.D. (lecturer)
prof. RNDr. Jaroslav Ramík, CSc. (lecturer)
Ing. Elena Mielcová, Ph.D. (seminar tutor)
Ing. Radomír Perzina, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Jaroslav Ramík, CSc.
Department of Informatics and Mathematics – School of Business Administration in Karvina
Contact Person: Mgr. Radmila Krkošková, Ph.D.

Prerequisites (in Czech)

K absolvování předmětu nejsou vyžadovány žádné podmínky a předmět může být zapsán nezávisle na jiných předmětech.

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

• Banking (programme OPF, B_HOSPOL)
• Business Economics in Trade and Services (programme OPF, B_EKOMAN)

Course objectives

The course objective is to teach the students basic principles of mathematical methods for modeling economical situations. The students should manage theoretical background of selected methods and models and be able to use Excel Solver and the program QSB for solving operational analysis problems on PC.

Syllabus

• 1. Principles and methods of Operational Analysis
  2. Linear programming: Introduction
  3. Economical and mathematical model of a linear programming problem, base solutions
  4. Linear programming: Solution
  5. Duality in linear programming models
  6. Integer linear programming
  7. Transportation problem
  8. Application of linear programming
  9. Graph Theory: basic principles and definitions
  10. Optimization problems on graphs: the shortest path and maximal flow algorithms
  11. Project management 1: Time analysis
  12. Project management 2: PERT
  13. Project management 3: Costs and sources
  1. Principles and methods of Operational Analysis
  History and principles of Operational Analysis, stages in application of Operational Analysis, classification of Operational Analysis branches.
  2. Linear programming: Introduction
  Economical and mathematical model, economical meaning of particular parts of mathematical model, basic elements of linear programming (LP), graphic representation of a feasible solutions set of a two-variables LP problem and solving the problem.
  3. Economical and mathematical model of a linear programming problem, base solutions
  General economical and mathematical model, economical meaning of particular parts of mathematical model, base solutions of a linear programming model
  4. Linear programming: Solution
  The principle of Simplex method, the number of LP problem optimal solutions determination, solving the LP problem by Excel Solver and QSB
  5. Duality in linear programming
  Duality as a relation between two LP problems, construction of dual problem, relations between primary and dual problem, economical interpretation of optimal solutions of both problems, sensitivity analysis.
  6. Integer linear programming
  Importance of integer and binary conditions, existence of integer optimal solution, assignment problem, basic principles of solving integer programming problems, solving the integer linear programming problem by Excel Solver and QSB.
  7. Transportation problem.
  Economical model of the transportation problem, mathematical model of the transportation problem, initial solution of the transportation problem, application of the transportation problem for production scheduling, solving the problem by Excel and QSB.
  8. Application of linear programming
  Construction of the mathematical model for the following problems: Cutting stock problem, Nutrition problem, Financial project analysis, Portfolio optimization problem, Production problem. Solving the problems by Excel and QSB. Interpretation of results.
  9.Graph Theory: basic principles and definitions
  Graph theory: basic elements, basic definitions, minimal spanning tree algorithm, Eulerian path .
  10. Optimization problems on graphs: the shortest path and maximal flow algorithms
  Shortest route and maximal flow problem, solving graph optimization problems by QSB.
  
  11. Project management 1: Time analysis
  Project graph, project analysis by critical path method - CPM
  12. Project management 2: PERT
  Project analysis by method PERT, basic characteristics of project analysis, i.e. mean value of activity time, standard deviation of activity time mean value of project completion time and standard deviation of project completion time, probability of finishing the project in planned time.
  13. Project management 3: Costs and sources, node
  Costs of activity realization, basic costs models, costs optimization of simple network project manually and by computer program QSB, problems of aggregation and desegregation of network graphs, possibilities of node evaluated network graphs.
  

Literature

recommended literature
• ALEVRAS, D., PADBERG, M. W. Linear Optimization and Extensions Problems and Solutions. Berlin: Springer, 2001. ISBN 3-540-41744-3. info
• SYDSAETER, K. STORM, A., BERCK, P. Economists' Mathematical Manual. Berlin: Springer, 2000. ISBN 3-540-65447-X. info
• WILLIAMS, H. P. Model Building Mathematical Programming. Chichester: John Wiley & Sons, 1993. ISBN 0-471-94111-5. info
• TAHA, H. A. Operations Research An Introduction. Englewood Cliffs: Prentice Hall, 1992. ISBN 0-13-187659-7. info

Teaching methods

Skills demonstration
Seminar classes

Assessment methods

Written exam

Language of instruction

English

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.

Teacher's information

test, 70% attendance at the seminars, exam test

Activity	Difficulty [h]
Ostatní studijní zátěž	41
Přednáška	26
Seminář	13
Zkouška	40
Summary	120

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