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Lecturer(s)
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Kolčavová Alena, Mgr. Ph.D.
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Zimola Bedřich, RNDr. Ph.D.
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Course content
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General overview of quantitative methods as management tools. Common characteristics of quantitative methods, procedure for solving operational research tasks, areas of application of operational research, methods and means, characteristics of individual quantitative methods. Mathematical programming. General mathematical and economic model of linear programming, typical models of optimization problems, duality. Simplex method. General shape of simplex table, interpretation of optimal solution, sensitivity analysis of optimal solution. Interpretation of dual variables. Distribution models of linear programming. General formulation of distribution tasks. Types of distribution tasks: assignment tasks, traffic problems, general distribution problem. Optimality criterion, transition to a new solution, degeneration of traffic tasks, alternative solutions. Methods for solving traffic problems. Northwest corner method, index method, Vogel approximation method. Finding a basic solution, optimality test, expression of an alternative solution. Stochastic models of economic processes. Stochastic models of the Markov type, stochastic processes with evaluation and their optimal control, continuous-time processes. Mathematical theory of collective service (queue theory). Basic elements and classification of collective service models, use of collective service models, methods of solving collective service models, simple exponential channel, multiplication and death processes, parallel arranged exponential channels, systems with finite number of elements. Optimization tasks in public service systems. Simulation analysis of public service systems. Kendall's notation. Inventory management models. Basic concepts, formulation of the task of inventory theory, classification of inventory management models, costs associated with the operation of inventory systems, characteristics of demand (or inventory consumption), deterministic dynamic model of inventory management, determining the optimal order size, Wilson's formula, optimal order size with respect to time needed to build inventory, inventory management models with price degression, stochastic inventory management models. Project management. Basic concepts of graph theory. Construction of a network graph for project management. Optimal paths in the graph. Basic tasks of network analysis - the shortest connection in the network, the shortest path in the network, the critical path method - time analysis of the network, time-cost analysis, cost-source analysis. CPM method - critical path method. Deterministic solution of project time analysis. Calculation of reserves. PERT method - stochastic method. Stochastic solution of project time analysis.
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Learning activities and teaching methods
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unspecified
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| prerequisite |
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| Knowledge |
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| mathematics - linear algebra |
| mathematics - linear algebra |
| applied statistics 1 |
| applied statistics 1 |
| Skills |
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| work with the software |
| work with the software |
| learning outcomes |
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| Knowledge |
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| explain the principle of modeling economic and managerial decision-making situations |
| explain the principle of modeling economic and managerial decision-making situations |
| describe the structure of the economic and mathematical model of linear programming and their mutual relationship |
| describe the structure of the economic and mathematical model of linear programming and their mutual relationship |
| explain the procedural steps when using the linear programming method (problem definition, economic model, mathematical model, solution, interpretation of results) |
| explain the procedural steps when using the linear programming method (problem definition, economic model, mathematical model, solution, interpretation of results) |
| describe the use of network analysis to support project management |
| describe the use of network analysis to support project management |
| explain the use of queuing theory models to determine the characteristics of mass service systems |
| explain the use of queuing theory models to determine the characteristics of mass service systems |
| describe individual inventory management models |
| describe individual inventory management models |
| Skills |
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| develop the economic and mathematical model of Linear programming for a specific decision-making situation |
| develop the economic and mathematical model of Linear programming for a specific decision-making situation |
| solve the mathematical model using QM software |
| solve the mathematical model using QM software |
| interpret the results of solving the mathematical model |
| interpret the results of solving the mathematical model |
| perform a time analysis of the project using the CPM method (duration, critical path, time reserves) |
| perform a time analysis of the project using the CPM method (duration, critical path, time reserves) |
| calculate the characteristics of the mass service system (probability vectors, utilization, average times spent in the system and in the queue, average number of units in the system and in the queue, losses) |
| calculate the characteristics of the mass service system (probability vectors, utilization, average times spent in the system and in the queue, average number of units in the system and in the queue, losses) |
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Recommended literature
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ANDRERSON, D., SWEENEY, D., WILLIAMS, T. An Introduction to Management Science - Quantitative Approaches To Decision Making. 10e. Thomson South-Western Publishing, 2003. ISBN 0-324-14563-2.
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BAGGIO, R., KLOBAS, J. Quantitative Methods in Tourism: A handbook. Bristol: Channel View Publications, 2011. ISBN 978-1-84541-173-2.
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CURWIN, J., SLATER, R., EADSON, D. Quantitative Methods for Business Decisions. 7th ed. Andover, UK: Cengage Learning, 2013. ISBN 978-1-480-6012-4.
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CHACKO, G. Operations Research/Management Science: Case Studies in Decision Making Under Structured Uncertainty. McGraw - Hill, 1993.
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LAWRENCE, J., PASTERNACK, B. Applied Management Science: A Computer-Integrated Approach for Decision Making.. Wiley, 1998. ISBN 0-471-13776-6.
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