Course code:  EMM 
Course title in language of instruction:  Ekonomicko matematické metody 
Course title in Czech:  Economicmathematical Methods 
Course title in English:  Economicmathematical Methods 
Mode of completion and number of credits:  Exam (6 credits) (1 ECTS credit = 28 hours of workload) 
Mode of delivery/Timetabled classes:  fulltime, 2/2 (hours of lectures per week / hours of seminars per week) parttime, 16/0 (lectures per period / seminars per period) 
Language of instruction:  Czech 
Level of course:  bachelor 
Semester:  WS 2017/2018 
Name of lecturer:  Ing. Martina Čampulová, Ph.D. (instructor) doc. Ing. Josef Holoubek, CSc. (examiner, instructor, lecturer, supervisor) Ing. Pavel Kolman, Ph.D. (instructor) 
Prerequisites:  Mathematics I 

Aims of the course: 
To learn, how to formulate, solve and interpret models of typical problems. For solving will be used linear programming and network analysis methods. 

Course contents: 
1.  Economic mathematical methods  principles, Linear programming problem (LP problem) (allowance 7/7)   a.  Fundamental terms definition, it's relation to system theory and system modelling  b.  LP problem formulation and properties, geometric and economic interpretation of LP problem  c.  Duality theory 
 2.  Simplex method (allowance 6/6)   a.  Simplex method  principle and algorithm  b.  Initial basic solution, simplex tableau, sensitivity analysis  c.  Dual simplex method 
 3.  Distribution problems (allowance 6/6)   a.  Transportation problems  methods, sensitivity analysis  b.  Container transportation problem, General distribution problem  c.  Assignment problem, Travelling salesman problem 
 4.  Special kinds of LP problems (allowance 3/3)   a.  Goal programming  b.  Integer programming  c.  Multicriterial optimization 
 5.  Graph optimization (allowance 6/6)   a.  Graph theory  fundamental terms  b.  Shortest path problem, Minimal spanning tree problem, maximum flow problem, Critical path method (CPM) 



Learning outcomes and competences: 
Generic competences:     ability to analyse and synthesize    ability to apply knowledge    ability to solve problems    ability to speak and write in mother tongue    basic computing skills    general knowledge    professional knowledge 
 Specific competences:     Student is able according to the character of the problem choose suitable method for its solving and to solve it.    Student knows clearly interpret result obtained by problem solving.    Student knows correctly construct mathematical or graphical model of solved problem.    Student will acquire basic Operations Research terminology and will be able to describe solving procedure of given problem. 


Type of course unit:  required 
Year of study:  Not applicable  the subject could be chosen at anytime during the course of the programme. 
Work placement:  There is no compulsory work placement in the course unit. 
Recommended study modules:   

Learning activities and study load (hours of study load): 
Type of teaching method  Daily attendance  Combined form  Direct teaching  lecture  28 h  0 h  practice  28 h  0 h  consultation  0 h  16 h  Selfstudy  preparation for exam  28 h  152 h  preparation for regular assessment  42 h  0 h  preparation for regular testing  42 h  0 h  Total  168 h  168 h 


Assessment methods: 
Three written 1/2 hour tests during semester verify knowledge and abilities. Tests are evaluated passed / not passed. Tests which were not passed students can make again. According to passed tests students get credit.
Written exam verifies ability of mathematical models formulation, solving and results interpretation. Furthermore, exam will verify knowledge of basic theoretical facts. Exam duration is 50 minutes. 

Recommended reading: 
Type  Author  Title  Published in  Publisher  Year  ISBN 

RQ  HOLOUBEK, J.  Ekonomickomatematické metody  Brno  Mendelova univerzita v Brně  2010  9788073754112  RQ  PLEVNÝ, M.  ŽIŽKA, M.  Modelování a optimalizace v manažerském rozhodování  Plzeň  Západočeská univerzita  2007  9788070434352  RE  JABLONSKÝ, J.  Operační výzkum : kvantitativní modely pro ekonomické rozhodování  Praha  Professional Publishing  2002  8086419231  RE  FIALA, P.  JABLONSKÝ, J.  Vícekriteriální rozhodování  Praha  VŠE  1994  8070797487  RE  STEVENSON, W J.  OZGUR, C.  Introduction to management science with spreadsheets  Boston  McGrawHill/Irwin  2007  9780072990669  RE  RAŠOVSKÝ, M.  Ekonomickomatematické metody  Brno  Mendelova zemědělská a lesnická univerzita v Brně  1999  8071574120  RE  HAVLÍČEK, J.  ZÍSKAL, J.  Ekonomicko matematické metody I  Praha  PEF Česká zemědělská univerzita  1998  8021304626 
