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Lecturer(s)
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Munzarová Simona, Ing. Ph.D.
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Course content
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1st week: Introduction to modeling. Mathematical modeling of complex decision processes, building models, finding solution, and implementation. Characteristics of operation research: system approach, team work, computer usage. 2nd week: Input-Output models. Basic and extended product models. Use of Input-Output models for planning purposes in supply management, production, and distribution of multi-stage chemical productions. 3rd week: Cost Input-Output models and their usage for costing of products and semi-finished products in multi-stage productions. 4th week: Introduction to Linear Programming. Formulating LP Models. Graphical and the Simplex solution methods. 5th week: Dual problem, dual simplex algorithm and shadow prices, postoptimality analysis, sensitivity analysis, determining bonds for optimal solution, parametric programming. 6th week: Transportation models, Assignment models. Fundamentals of Nonlinear Programming. 7th week: Overview of different problems that can be solved using graph theory. Network models for time coordination of complex projects. Shortest Path Problem. CPM and PERT models. Simulation in stochastic graphs. 8th week: Using network models in analyzing sources, problems of balancing sources. Cost analysis in networks, optimization. 9th week: Inventory models. Deterministic inventory models computing the optimal order quantity. Stochastic inventory models. 10th week: Queuing models. Single-Server Model, Multiple-Server Model, economic analysis of Queuing systems, optimizing number of operators. 11th week: Equipment Replacement Problems solved by dynamic programming - equipment that wear down and equipment that break down. 12th week: Decision Making Theory. Basic scales for classification, measurement and evaluation of variants. Decision Making problems with Multiple Objectives. 13th week: Decision Making under Uncertainty. Axioms and principles of Decision Making in risk situations. Stochastic decision trees. 14th week: Game theory. Problems classification. Two-Person Zero-Sum and Constant-Sum Games: Saddle Points; Randomized Strategies; Domination. Introduction to n-person game theory.
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Learning activities and teaching methods
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unspecified, Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Methods of individual activities
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Learning outcomes
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The course focuses on mathematical modeling and optimization of complex managerial decision problems in business economy and operations management. The course follows up Math and Statistics classes, and develops, deepens and integrates knowledge in business economy and other economy-managerial classes. In seminars, students practice different methods solving examples using PC and MS Excel. Attention is paid to the interpretation and implementation of models in practice.
Students gain the skills to formulate managerial decision problems as mathematical models, gain the ability to choose appropriate methods for their solution and to find optimal respectively effective solutions using Excel and to interpret the obtained results, including sensitivity analyzes.
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Prerequisites
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A prerequisite for studying the subject is knowledge of mathematics, business economics and business management at the undergraduate level.
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Assessment methods and criteria
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Oral examination, Didactic test, Self project defence, Presentation
Knowledge and skills are verified by written and oral exam. It examines the rate of acquired knowledge and application skills.
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Recommended literature
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Albright, S. C., Winston, W. L. Management Science Modeling, 3rd edition, South-Western Cengage Learning, ISBN 0-324-66346-3.
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Anderson, Sweeney, Williams, Camm, Martin. Quantitative Methods for Business, 12th edition, South-Western Cengage Learning, ISBN 1-133-58446-2.
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Render, B., Stair, R. M. Jr., Hanna, M. E. Quantitative Analysis for Managers, ninth edition, Pearson, Prentice Hall, 2006, New Jersey ISBN 0-12-153688-5.
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