Operations Research

Course goal is overwhelm with academic and scientific methods and quantitative techniques for obtaining alternative (optimal) solutions of real world problems on which basis user can perform analysis and synthesis of given solutions, make decision and predict consequences.

Solution of concrete problems with application of scientific methods, procedures and techniques using analysis, synthesis and prediction of solutions and consequences as well as overwhelm with methods, procedures and research processes and application of knowledge (gained skills) in practice.

Introduction. Problem classification. Linear programming (graphical solution, simplex method, dual theory, sensitivity analysis). Transportation problem (open and closed). Linear regression (Least square method). Nonlinear programming (definition of convex function and set, one-variable and multivariable unconstrained and constrained optimization, Karush-Kuhn-Tucker (KKT) conditions, Gradient Search Procedure). Quadratic programming. Dynamical programming, Project management (structure analysis, time analysis using PERT/CPM, critical path, cost analysis – PERT/Cost). Service systems – Queuing theory (queuing theory models – single and multi server with out and with partial and complete help between servers, with finite and infinite source of customers, optimisation of service systems). Simulation of service systems (approach to simulation, Monte Carlo method, generation of random numbers, processing and presentation of simulation results).

Audit lessons (examples of linear programming, transportation problem, linear regression, nonlinear programming, quadratic programming, dynamical programming. Examples of project management – structure analysis, time analysis cost analysis. Examples of application of queuing theory models – finite and infinite source of customers, single and multi server without and with partial and complete help between servers. Examples of service system optimisation. Application of simulation and Monte Carlo method in analysis and modelling of service systems. Examples from area of decision making and forecasting). Laboratory work (use of adequate software).

There is no special conditions needed for course attending

1. Bugaric, U.: Lecture handouts, Faculty of Mechanical engineering Belgrade, Belgrade, 2008-2011. 2. Bugaric, U., Petrovic, D.: Servicing system modelling, Faculty of Mechanical engineering Belgrade, Belgrade, 2011. 3. Bugaric, U.: Methodology for analysis of single position machines work, Foundation Andrejevic, Belgrade, 2003. 4. Software: QtsPlus 3.0 (Queuing theory software Plus). 5. Software: QSopt Version 1.0 (Linear programming problems). 6. Software: IOR Tutorial (Interactive Operations Research). 7. Software: MS – Project (Project management). 8. Personal computers.

Total assigned hours: 65

New material: 30
Elaboration and examples (recapitulation): 0

Auditory exercises: 20
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: 0
Test: 10
Test: 0
Final exam: 5

Activity during lectures: 10
Test/test: 60
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 30

Petrić, J.: Operations Research (book 1 & 2), Savremena administracija, Belgrade, 1990.; Žiljak, V.: Computer simulation, Školska knjiga, Zagreb, 1982.; Clymer, J. R.: Systems analysis using simulation and Markov models, Prentice-Hall International Inc., 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.