M3160 Mathematics for sustainable planning

Faculty of Science
Autumn 2025
Extent and Intensity
2/1/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
In-person direct teaching
Teacher(s)
Mgr. David Kruml, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 M4,01024
  • Timetable of Seminar Groups:
M3160/01: Wed 16:00–16:50 M4,01024, D. Kruml
Prerequisites
! MHTOK Value stream modeling
Knowledge of the basic concepts of set, representation, relation, graph at the level of M1120 Discrete Mathematics and random variables at the level of M3121 Probability and Statistics I.
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
Course objectives
The aim of the course is to introduce students to the modeling of value flows and their mathematical formalization.
Learning outcomes
A student will be able to convert a specific procedural task into a formal form and propose a method of its solution. The student will know the causes of losses and methods of their quantification.
Syllabus
  • Plan and its implementation: sources, recipes, conditionality, collisions.
  • Processes and stacks: process parameters, material work in progress, equipment states.
  • Sustainability principles: returns, externalities, resource use.
  • Hierarchical flow breakdown: breakdown structures, aggregation, composite states.
  • Mathematical description of flow: graphs, categories, Petri nets.
  • Causes of wastage: muda, mura, mudi, defect concept, multicriteria decision making.
  • Algorithms: validation, optimization, simulated annealing.
  • Random effects: process variability, parameterization and summation of independent variables, entropy.
  • Data representation of flow: parameter breakdown, markup languages, principles of algorithmic flow processing.
Literature
  • HOPP, Wallace J. and Mark L. SPEARMAN. Factory physics. 3rd ed. Long Grove, Ill.: Waveland Press, 2008, xxv, 720. ISBN 9781577667391. info
Teaching methods
The course is taught in the form of a lecture and joint problem solving in exercises. At the end of the semester, the course includes a presentation of student projects.
Assessment methods
The course is completed by defending a simple project and passing a test; it is necessary to obtain at least 40% points in the test.
Language of instruction
Czech
Study support
https://is.muni.cz/auth/el/sci/podzim2025/M3160/um/
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The study course was created with the support of the EU, Next Generation, the National Recovery Plan (NPO), and the Ministry of Education, Youth and Sports, as part of the project NPO 7.4. – Support for Green Skills and Sustainability at MU, Reg. No. 0016/NPO74_PZDU_VS.
  • Enrolment Statistics (recent)
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