- •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?
52. What is the goal of the assignment problem? What are the prerequisites?
Goal is to get 0 in each row and column, find the distance(shortest)-not path!!!
53.What is the goal of the travelling salesman problem? The aim is to find a simple cycle containing all nodes and minimizing the total distance. How to travel through all places(nodes), come back and travel with the shortest way.
54. How can be applied the Vogel approximation for the travelling salesman problem?
We calculate the difference between the two lowest-cost arcs leaving an origin or entering a destination.
We choose the field(arc) that has the lowest cost in that row or column having the greatest cost difference (add this arc into the tour). Then we delete all the other connections in the line and column of the chosen field. Delete the connection which closes the circle before all places are included.
55.Describe the maximal flow problem and its solution.
We have to find the pipes (trupky) of positive capacity P from the source to the sink, be a saturating path ( one or more arc capacity is fully used). How much water can flow from A to Z? Reduce all capacities along the pipes, by the value of P.Repeat the entire process until no pipe of positive capacity exists from the source to the sink.
56.Describe the shortest path problem and its solution.
The goal is to find a path through that has the shortest total distance. To this I use dijsktra algorithm.
57. Describe the Dijkstra algorithm. For what it is applied?
Task is to compute the shortest path from one node to other network nodes.
Steps: 1)set the distance for the source node to zero, and set all other nodes to infinity
2)mark all nodes as unvisited. Set the source node as a current one.
3)for a current node, consider all its unvisited neighbours and compute their distance from the source node
4)choose the unvisited node whose distance is shortest, and set it to a current node. Mark the previous current node as visited. A visited node will not be checked anymore.
5)if all nodes have been visited, the process is finished. Otherwise, repeat from step 3).
At the end I choose the lowest number of final destination.
What is a project? What are the main parts of the project?
What is the critical task in the project?
Describe the graph used in the critical path method.
Describe the graph called network.
What is the critical path in the project management?