OPF:MMEPOANA Operational Analysis - Course Information

MMEPOANA Operational Analysis

Extent and Intensity

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

Teacher(s)

Ing. Elena Mielcová, Ph.D. (lecturer)
Ing. Radomír Perzina, Ph.D. (lecturer)
Ing. Filip Tošenovský, Ph.D. (lecturer)
Ing. Elena Mielcová, Ph.D. (seminar tutor)
Ing. Radomír Perzina, Ph.D. (seminar tutor)
Ing. Filip Tošenovský, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Jaroslav Ramík, CSc.
Department of Informatics and Mathematics – School of Business Administration in Karvina

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

there are 7 fields of study the course is directly associated with, display

Course objectives (in Czech)

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 (in Czech)

• 1. Principles and methods of Operational Analysis
  2. Economical and mathematical model of a linear programming problem and its graphical interpretation
  3. Solving the linear programming problem
  4. Application of linear programming
  5. Duality in linear programming
  6. Transportation problem
  7. Integer linear programming
  8. Optimization problems on graphs
  9. Project management 1: Time analysis
  10. Project management 2: PERT, GERT
  11. Project management 3: Costs and sources, node evaluated network graphs
  12. Queuing models
  1. Principles and methods of Operational Analysis
  Principles of Operational Analysis, stages in application of Operational Analysis, classification of Operational Analysis branches.
  2. Economical and mathematical model of a linear programming problem and its graphical interpretation
  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. Solving the linear programming problem
  The principle of Simplex method, the number of LP problem optimal solutions determination, solving the LP problem by Excel Solver and QSB.
  4. 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.
  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. 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.
  7. 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.
  8. Optimization problems on graphs
  Graph theory basic elements, minimal spanning tree, shortest route and maximal flow problem, solving graph optimization problems by QSB.
  
  9. Project management 1: Time analysis
  Project graph, project analysis by critical path method - CPM manually and by the computer program QSB.
  10. Project management 2: PERT, GERT
  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.
  11. Project management 3: Costs and sources, node evaluated network graphs
  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.
  12. Queuing models
  Queuing systems, characteristics and structure of queuing systems, simple exponential queuing model - M/M/1, exponential model with parallel lines - M/M/c, optimization of queuing models, solving of queuing systems with QSB.
  

Literature

required literature
• RAMÍK, J., ČEMERKOVÁ, Š., MIELCOVÁ, E. Operační analýza pro ekonomy. Karviná, OPF SU, 2004. ISBN 80-7248-199-3. info
• TAHA, H. A. Operations Research An Introduction. Englewood Cliffs: Prentice Hall, 1992. ISBN 0-13-187659-7. info

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
• WISNIIEWSKI, M. Quantitative Methods for Decision Makers. London: Pitman Publishing, 1997. ISBN 0-273-62404-0. info
• WILLIAMS, H. P. Model Building Mathematical Programming. Chichester: John Wiley & Sons, 1993. ISBN 0-471-94111-5. 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.

• Enrolment Statistics (Winter 2012, recent)
  
• Permalink: https://is.slu.cz/course/opf/winter2012/MMEPOANA