Operation Research

  • Code:  
  • Number of credits:  5
  • Subject coordinator:
    Victor GORELIK
  • Lecturers: Viktor GORELIK,
    Dmitriy BORODIN
  • Credit contract possible:  Yes
  • Examination contract possible:  Yes
  • Teaching language:  English, Russian


 Course Activity: 
  • Lectures
  • Practical Classes
  • Lab Classes


 Course unit type: 
  • Specializing



  1. General definitions and mathematical model of the operation
  2. Standard optimization problems
  3. Linear programming
  4. Nonlinear programming
  5. Dynamic programming
  6. Multiple criteria optimization
  7. Games in the normal form
  8. Positional games
  9. Waiting line systems



 A. General competences 

PB - 01. Intellectual and cognitive capacities
PB - 02. Acquisition and processing of information


 PB – 01. The student is able to construct mathematical models of real decision-making processes.

PB – 02. Depending on the model type and source information the student is able to choose and use the mathematical methods of analysis and optimum seeking.

  B. Profession-oriented/ General scientific competences  


  • Know general problems of the operations research: linear programming, nonlinear programming, vector optimization, game theory, decision-making in uncertain and stochastic environment.
  • Being able to classify the real life decision problems according to the general operations research sections
 C. Profession-specific competences  
  •  Being able to introduce general methods of linear programming (simplex method, Hungarian method, potentials method, northwest corner method), of nonlinear programming (Lagrange method, Kuhn-Tucker conditions, duality theorem), of vector optimization (Paretooptimality, criteria convolution methods, ideal point method, analytical hierarchy process, method of successive averages), of solving matrix games (bringing to linear programming, Braun rule, Shapley-Snow rule)
  • Being able to introduce the advanced methodology and tools of operations research to assist decision-making. Build and verify models of real life decision problems of industry, trade and finance, select the most suitable solution methods and computational tools (Mathcad, Mathlab), derive a solution from the model, evaluate, interpret and present the results.
  •  Being able to analyze a practical problem and to translate it into an optimization model. Being able to show the advantages and disadvantages of the different solution techniques. Being able to use optimization software (Mathcad, Mathlab, Microsoft Excel, Microsoft Project) for the analyses of the problem under study.
 D. Scientific competences 



  Being able to apply the operations research methodology in scientific research and for real life decision in industry, economical, ecological and financial fields.



 A. Previously required courses 

Mathematical Analysis, Algebra, Theory of Probability and Mathematical Statistics, Discrete Mathematics, Numerical Methods

  B. Required competences  

Mathematical Analysis: the methods of working with analytical functions.
Algebra: the calculation with letters, matrices and special products, solving of equations of the first, second and n-degree, solving of simultaneous equations.
The Differential Analysis: finding derivations of the first and second degree and complex derivations, working with integrals of the first degree.
Theory of Probability and Statistics: theorem of probability calculation, expectation function and variance, the law of large numbers, regression analysis method, statistical criteria.

Calculation methods: branch-and-bound method, set of equations solving methods.


 Educational tools:

 A. Type 
  •  Course
  •  Labs
  •  Textbooks
  •  Online learning platforms (dokeos, private lecturer website)
  •  Internet
  •  mathematical computing systems
  B. Obligatory educational tools  
  1. Course book: Viktor GORELIK, Tatiana FOMINA “Introduction to Operations Research”, published by Moscow state pedagogical university and Lipetsk state pedagogical university in 2004.
  2. Mathematical computing systems: Mathcad, Mathlab
 C. Recommended educational tools 

 Operations Research Models and Methods, by Paul A. Jensen and Jonathan F. Bard, published by John Wiley and Sons in 2003.

Free online Operations Research books:
(last accessed on March 5th, 2009)


Optimization software: Microsoft Excel, Microsoft Project

Online learning platform: http://dokeos.mpgu.edu


 Teaching methods : 

 A. Type 
  • Lectures
  • Practical Classes
  • Lab Classes
  • Other: higher education on distance
  B. Description  

This course is taught in English or Russian

Plenary lectures: 36h = 2h per week during 18 weeks during the first semester.

Practical Classes (obliged): 18h = 2h per two weeks during 18 weeks during the first semester.

Lab Classes: (obliged): 18h = 2h per 2 weeks during 18 weeks during the first semester.

Higher distance education: for this course, an extra syllabus is available, containing guidelines how to study the material in an optimal way.


 Assessment : 

 A. Type 
  • permanent (written tests during semester)
  • oral examination
  • evaluation
  B. Description  

Total number of credits: 5 credits
Period of examination 1 (first chance)
PR: 3 credits - 1 oral assessment
PR labs: 1 credit - permanent and several computing assessments
PR practical classes: 1 credit - permanent and several written assessments
Different approach: 1 oral exam, the mark you get for the exam gives you the corresponding number of credits: 5 credits for A, 4 credits for B and 3 credits for C.

Examination contract:
1 written assessment for the OR. The mark obtained in this examination is the result of the OR and the OR labs.

Higher distance education:
1 written assessment for the OR. The number of credits obtained in this examination is the result of the OR written examination.


 Teaching support : 

Extra course OR: 2h per week during 18 weeks during the first semester.
Higher distance education: for this course, an extra syllabus is available, containing guidelines how to study the material in an optimal way.