Achieving competency and enhancement of gained knowledge in academic studies in fields of modelling, optimisation and forecasting for needs and implementation in Industrial engineering, as well as development of creative skills and overwhelm with practical skills needed for professional practice in solving real world problems of Industrial engineering.

Curriculum overcome enables coverage of overall skills as analysis and synthesis of real world problems in industry using mathematic tools underlying: modelling (mathematical modelling of real world system), optimisation (gaining optimal configuration of real world system) and forecasting (work of real system in future).

Modelling – What is mathematical modelling ? (or how to translate our beliefs about how the world functions into the language of mathematics). Division of mathematical models (deterministic, stochastic). Range of objectives obtained using mathematical modelling (developing scientific understanding, test the effect of changes in a system, aid to decision making). Optimisation – Optimisation as an mathematical discipline. Finding of minimal and maximal values of goal functions subject to constrains. Overview of optimisation methods. Forecasting – Time series, Forecasting methods, Forecasting errors, Regression analysis (linear regression, method of least squares), Forecasting in practice.

Selection of real world industrial system connected with candidate research, which should be used as a basis for system modelling, optimisation and forecasting.

Students should have (but not necessary) a background in statistics, system engineering, mathematics, computer science.

1. Software: QtsPlus 3.0 (Queuing theory software Plus). 2. Software: QSopt Version 1.0 (Linear programming problems). 3. Software: IOR Tutorial (Interactive Operations Research). 4. Software: MS – Project (Project management). 5. Personal computers.

Total assigned hours: 65

New material: 40
Elaboration and examples (recapitulation): 10

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 10
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 70
Final exam: 30
Requirement for taking the exam (required number of points): 0

Petrić, J.: Operations Research (book 1 & 2), Savremena administracija, Belgrade, 1990.; Churchman, C. W., Ackoff, R. L., Arnoff, E. L.: Introduction to Operations research, John Willey & Sons Inc., 1957.; Hillier, F. S., Lieberman, G. J.: Introduction to operations research (seventh edition), McGraw-Hill, New York, 2000.; Bugaric, U., Petrovic, D.: Servicing system modelling, Faculty of Mechanical engineering Belgrade, Belgrade, 2011. . ; Bugaric, U.: Methodology for analysis of single position machines work, Foundation Andrejevic, Belgrade, 2003