Operations Research (System Analysis)

Type: Normative

Department: theory of optimal processes




SemesterAmount of hoursLecturerGroup(s)
736ArrayPMa-41, PMa-42
814Professor M. Ya. BartishPMa-41, PMa-42

Laboratory works

SemesterAmount of hoursGroupTeacher(s)
718PMa-41L. V. Nykolaichuk
PMa-42Senior Researcher B. M. Holub, Associate Professor A. V. Melnychyn
828PMa-41L. V. Nykolaichuk, N. P. Ohorodnyk
PMa-42L. V. Nykolaichuk, N. P. Ohorodnyk

Course description

Aim. Provide students with knowledge of basic concepts, principles and methods of mathematic modelling operations, introduce the typical research tasks ion operations research (OR) under certainty, uncertainty and conflict of intersects (game theory) and methods of their solution.

Summary. Subject OR. Classification and description of the problem OR methods for solving problems specific class. Determining efficient (by Pareto) and littleefficient (by Slater) solutions of problems of multicriteria optimization and forming a single compromise criterion. Decision-making under risk. Decision-making for total uncertainty. The adoption decision in conflict interests of decision-makers. Normal and expanded forms of the game. Static and positional game. Basic concepts of solutions in static games: dominance strategies, Nash equilibrium in pure and mixed strategies. Saddle point and maksymin / minimax strategies of players in antagonistic games. By reverse induction positional games with perfect or nearly perfect information. Convert the expanded form of the game to normal. Deterministic oneresources static model of inventory control with periodic or continuous supply of the absence / presence of scarce resources. Potential method for solving the transport problem. Combinatorial optimization problems and methods of their solution (branch and bound, dynamic programming, greedy).

Target. Teach students: methodology OR to use for managerial decisions in various fields of human activity, classify typical problem OR, choose the method of solving the problem OR according its class, check the conditions of convergence of methods and analyse the results.

As a result of studying this course, the student should:

know: typical model problem OR, theoretical foundations, areas and features use methods of operations that are used for solving these tasks, sub-tasks OR the examples with effective solutions with a priori estimates of proven quality;

be able to: build mathematical models based on the formulation of the problem of decision-making in a particular subject area of ​​human activity, classify obtainment problems OR and choose the appropriate method of solution; apply of operations research to specific problems OR, analyse the results and provide them with relevant content interpretation.