- •1 Introduction to operations research
- •Explain the terms:
- •What is the matrix form of the system of linear equations?
- •X column vector with n entries;
- •Apply the Frobenius theorem in the solution of the system of linear equations.
- •Describe the algorithm of the Gauss-Jordan total elimination.
- •Describe the algorithm of finding the inverse matrix.
- •Which are the phases of the decision making process?
- •Describe the Anthony´s classification of the decision making. Draw the Anthony´s pyramid.
- •Which are the typical features of the strategic planning, tactic planning and operational control?
- •Compare programmed and non programmed decisions.
- •Compare the main kinds of the mathematical models (operational exercise, gaming, simulation, analytical model).
- •11. Which are the main types of the variables in the mathematical model?
- •11. Describe the process of formulation and application of the linear programming model.
- •What is the goal of the linear programming model?
- •2 Introduction to linear programming
- •14. Describe the constraints and the objective function in the linear programming model.
- •15.Which are the basic groups of applications of the linear programming model?
- •3 Applications of linear programming
- •18. Which are the phases of application of the linear programming model?
- •19.Describe the steps in the graphical solution of the linear programming model.
- •20.What is the graphical presentation of the feasible region?
- •21. Which solutions of the lp model are feasible, which are optimal and which are suboptimal?
- •23. What is a shadow price on a constraint? In graphical representation.
- •38. Describe the process of solution (steps) of the transportation problem.
- •39. What is the number of basic and decision variables in the transportation problem?
- •40.Describe the optimality test in the transportation problem. Which information it provides?
- •40. What is the purpose of the Dantzig loop (closed path)?
- •41.How do we solve the situation when the sum of sources is not equal to the sum of demands?
- •43. How do we solve the situation when one or more communication routes are not available?
- •44. How do we solve transportation problems with degeneration?
- •7 Graph theory
- •47. Describe the graph called Hamiltonian circuit. In which method it is applied?
- •8 Network models
- •50.What are the differences between the transportation problem and assignment problem?
- •51.What is total opportunity cost matrix? In which method it is used? How does it look?
- •52. What is the goal of the assignment problem? What are the prerequisites?
- •54. How can be applied the Vogel approximation for the travelling salesman problem?
- •55.Describe the maximal flow problem and its solution.
- •56.Describe the shortest path problem and its solution.
- •57. Describe the Dijkstra algorithm. For what it is applied?
Which are the typical features of the strategic planning, tactic planning and operational control?
Which are the typical decisions in those groups?
Strategic planning:,extremely important, long-time long-lasting effect - uncertainties and risk attitudes (more than 3 years), nonrepeatable, high uncertainity,aggragated info, managerial policies - high managerial level, Examples: major capital investments in new production capacity and expansions of existing capacity, determination of location and size of new plants, distribution facilities, development and introduction of new products, and issuing of bonds and stocks.
Tactic planning: medium time (1-3 years), significant aggregation of info, The basic problem to be resolved is the effective allocation of resources (e.g., production, storage, and distribution capacities; work-force availabilities; marketing, financial, and managerial resources) to satisfy demand and technological requirements
Operational control: day-to-day, after making an aggregate allocation of the resources of the firm, it is necessary to deal with the day-to-day operational and scheduling decisions. complete disaggregation of the information generated at higher levels into the details consistent with the managerial procedures followed in daily activities, at this level are the assignment of customer orders in the work shop, inventory accounting and inventory control activities, dispatching, expediting and processing of orders, vehicular scheduling, and credit granting to individual customers.
Compare programmed and non programmed decisions.
Programmed decisions are those that occur routinely and repetitively, they can be structured, they can be delegated on the lower echelons of the organization.
Nonprogrammed decisions are complex, unique, and unstructured, large amount of good judgment and creativity, normally, top managers are responsible
Compare the main kinds of the mathematical models (operational exercise, gaming, simulation, analytical model).
Operational exercise: operates directly with the real environment in which the decision is under the study, the modeling involves (zahrnuje) designing (navrhování) a set of experiments to be conducted (prováděny) in that environment, and measuring and interpreting the results of those experiments, research in the natural sciences, observations of a given phenomenon (jev),Operational exercises are on highest degree of realism of any form of modeling approach, and are expensive to implement (realizovat).
gaming: representation of the real environment. The model is simply a device that allows the decision-maker to test the performance of the various alternatives. However, the cost of processing each alternative has been reduced, and the speed of measuring the performance of each alternative has been increased, is used mostly as a learning device
simulation: the models are similar to gaming models except that all human decision-makers are removed from the modeling process, many simulation models take the form of computer programs, where logical arithmetic operations are performed in a prearranged sequence.
analytical model: problem is represented completely in mathematical terms, normally by means of a criterion or objective, which we seek to maximize or minimize, subject to a set of mathematical constraints that portray (zobrazit) the conditions under which the decisions have to be made, the model computes an optimal solution, that is, one that satisfies all the constraints and gives the best possible value of the obj. fun.