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Lecturer(s)
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Linda Bohdan, doc. RNDr. CSc.
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Course content
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Convex sets. Definition of linear programming tasks, creation of mathematical models. Graphical solution of linear programming tasks. Canonical form of linear programming task, forms of notation with the accent put on matrices notation, terminology, basic theorems about set of all acceptable solutions. Simplex method. Simplex table, algorithm of the Simplex method. Modification of the models of linear programming tasks into canonical form, addition variables. Artificial base. Modification of the Simplex algorithm. Duality. Definition of dual task, duality theorems, searching for a solution of dual task, economical interpretation of duality. Analysis of the sensitivity of linear programming tasks with regard to the coefficients cj, bi, aij. Integral programming, Gomorys´ algorithms. Transportation task, Dantzig's algorithm. Methods searching for initial solution. Assignment problem, Hungarian method. Non-linear programming, basic terms. Principles of multicriterial programming. Basic terms in the theory of graphs, algorithms searching for ultimate ways in the graphs. Network graph CPM, PERT.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Methods of individual activities
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Learning outcomes
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The aim of the course is to acquaint the students with optimization methods in the sphere of mathematic programming and network analysis. Students will learn to create the selected mathematical models and solve these models.
Student acquires skills to solve some decision-making situation by the help of exact methods from the areas of mathematical programming and control of extended projects.
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Prerequisites
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Prerequisite for successful mastering of this subject is knowledge of mathematics within the range taught at universities.
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Assessment methods and criteria
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Written examination, Student performance assessment
Assignment-completion of all given tasks and passing all written tests. Examination-comprises of two parts, practical exercises and theoretical part (at least 51% success rate in each part is required).
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Recommended literature
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Hillier,S.F.,Lieberman,G.J. Introduction to Operations Research. McGraw Hill, 2001. ISBN 0-07-121744-4.
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