Course code:  EMMA 
Course title in language of instruction:  Economicmathematical Methods 
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) 
Language of instruction:  English 
Level of course:  bachelor 
Semester:  WS 2019/2020 
Name of lecturer:  Ing. Martina Čampulová, Ph.D. (examiner, instructor, lecturer) doc. Ing. Josef Holoubek, CSc. (supervisor) 
Prerequisites:  Mathematics I or Mathematics I 

Aims of the course: 
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, 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 kind of LP problems (allowance 3/3)   a.  Goal programming  b.  Integer programming  c.  Multicriterial optimization. 
 5.  Graph optimization (allowance 6/6)   a.  Graph theory  fundametal 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  Direct teaching  lecture  24 h  practice  24 h  Selfstudy  preparation for exam  36 h  preparation for regular assessment  84 h  Total  168 h 


Assessment methods: 
Written test (including theoretical and practical part) at the end of the course. Additional requirements (attendance, seminar work, etc..) are not set. Students can take on the exam calculator. To pass the exam, students must obtain at least 55% of available points. 

Recommended reading: 
Type  Author  Title  Published in  Publisher  Year  ISBN 

RQ  STEVENSON, W J.  OZGUR, C.  Introduction to management science with spreadsheets  Boston  McGrawHill/Irwin  2007  9780072990669  RE   Optimization in operations research  Upper Saddle River, N.J.  Prentice Hall   0023984155  RE  FÁBRY, J.  Management science  Praha  Oeconomica  2003  802450586X 
