Management Science

Garant předmětu:

Petr Makovský

Lecturer:

Petr Makovský, Jiří Nárožný

Tutor:

Petr Makovský, Jiří Nárožný

Supervisor:

Institute of Economic Studies

Synopsis:

Management Science is a scientific discipline that deals with the formulation, modelling and solution of a variety of decision-making problems, especially of an optimization nature.

Requirements:

Successful completion of the course requires earning credit and passing a written exam. Earning credit resides on attendance at a maximum of three regular absences per semester* and the writing of a written credit check

for at least 50% of the maximum number of points. The credit check is written approximately halfway through the semester.

A written examination paper is considered passed if at least 50% of the maximum points are achieved.

*Extraordinary absences for which the student provides relevant reasons are not included in this number of absences. In such situations, the instructor may request supporting documents to verify them.

Syllabus of lectures:

1. Introduction to the course. Linear programming. Construction of mathematical models. General rules in constructing mathematical models. Basic type problems - production program, cutting plan, mixing problem, investment problem. Building models in practice.

2. Basic methods of linear programming. Matrix notation of a system of equations. Basic solution of a system of equations. Canonical form of the linear programming problem. Modification of boundary conditions from inequalities to equations with negative right-hand side. Admissible basic solution of a linear programming problem.

3. Graphical solution of the linear programming problem. Basic principles of graphical solution, graphical solution procedure.

4. Simplex method of solving a linear programming problem - solving by simplex algorithm. Matrix notation of the simplex table.

5. Sensitivity analysis. Sensitivity analysis of the right-hand side of constraints. Sensitivity analysis of the coefficients of the objective function.

6. Introduction to integer programming. Method of cutting superplanes. Gomorih algorithm I and II. Integerity requirement on all or some selected structural variables.

7. Transport problem. Formulation of the transport problem. Finding the initial basic solution of the Traffic problem - the „northwest corner“ method, the Index method.

8. VAM (Vogel Approximation Method). Dantzig optimization method.

9. Assignment problem. Formulation of the minimization and maximization problem. Hungarian method for solving the Assignment problem. Finding the optimal permutation.

10. Graph theory. Basic concepts of graph theory. Graph representations. Skeletons, trees, paths in graphs. Isomorphism of graphs.

11. Searching in oriented and unoriented graphs. Graph algorithms. Maximum path search. Determination of maximum flow - throughput in a traffic network. Floyd's algorithm.

12. Network analysis I. CPM method - critical path method. PERT method. Determination of time reserves.

13. Introduction to inventory theory. Multi-criteria decision making.

14. Mass service models. Markov models.

Syllabus of tutorials:

1. Building mathematical models. Practicing basic types of linear programming problems.

a) Production program

b) Cutting plan

c) Mixing problem

d) Investment problem

2. Finding a basic solution to a system of linear equations using methods from linear algebra. Examples of finding an admissible basic solution to a linear programming problem.

3. Graphical solution of a linear programming problem. Machine solution of a linear programming problem (MS Excel, LINGO)

4. Simplex method of solving a linear programming problem. Solution using matrix notation of simplex table.

5. Sensitivity analysis of the right-hand side of constraints. Sensitivity analysis of the coefficients of the objective function.

6. Problems leading to integer linear programming.

7. Transportation problem. Formulation of the transport problem. Finding the initial basic solution of the traffic problem - the „northwest corner“ method. The index method.

8. VAM (= Vogel Approximation Method). Dantzig optimization method.

9. Assignment problem. Formulation of the minimization or maximization problem. Hungarian method of solving the assignment problem. Finding the optimal permutation.

10. Graph theory. Graph representation. Skeletons, trees, paths in graphs. Graph isomorphism.

11. Searching in oriented and non-oriented graphs. Graph algorithms. Maximum path search. Determination of maximum flow - throughput in a traffic network. Floyd's algorithm.

12. Network analysis. Determination of the critical path. Construction of network graph.

13. Introduction to inventory theory. Multi-criteria decision making.

14. Mass service models. Markov models.

Study Objective:

The general objective of the course is to teach students to develop and solve mathematical models of real (primarily economic) systems with an emphasis on finding optimal decisions

according to selected criteria. The students will be introduced to the basic methods of linear programming, the application of simplex algorithm and dual simplex algorithm will be explained using concrete examples.

Further in the course there will be explained the Transportation problem with the objective of minimizing transportation costs and the Assignment problem with the application of Hungarian method to find the optimal assignment.

Next, students will be introduced to basic concepts in graph theory, in particular graph representation, finding graph skeletons, paths or permeability in graphs, graph algorithms in

oriented and non-oriented graphs. It will also include issues of network analysis, especially the application of the CPM method.

In the final part of the semester, students will be introduced to the more advanced parts of Management Science, including the theory of inventories, bulk handling, multi-criteria

decision making and Markov processes.

Study materials:

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2018). An introduction to management science: quantitative approach. Cengage learning.

Note:

Time-table for winter semester 2023/2024:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomDEJ:422 12:30–14:00 (parallel nr.101) Dejvice Učebna
Wed	roomDEJ:204 12:30–14:00 (lecture parallel1) Dejvice Učebna roomDEJ:204 12:30–14:00 (lecture parallel1) Dejvice Učebna
Thu
Fri

Time-table for summer semester 2023/2024:

Time-table is not available yet

The course is a part of the following study plans: