- •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?
44. How do we solve transportation problems with degeneration?
Degeneracy problem is when the number of filled cells is less than number of columns minus one (m+n-1) Degeneracy appears at the moment when we cross the row and column at the same time(while finding initial solution) we need to add (occupy) more cells. M must be placed somewhere in row/ column where the degeneracy appeared, preferably to the cells with the lowest distance
7 Graph theory
45. Describe the graph called network. It is a connected graph, free of circuits. Weight with positive weights. Has exactly one starting point(it is single sourced) and one final point(eg sink)
46. Describe the graph called spanning tree. A tree whose edge (okraj) set is a subset of the edge set of the graph - at any undirected connected weighted graph, there is a minimum spanning tree, subgraph of a tree type with minimal sum of arc weights.
47. Describe the graph called Hamiltonian circuit. In which method it is applied?
Circuit through all arcs=a graph cycle(ie closed loop) through a graph that visits each node exactly once, the problem of finding an optimal Hamilton circuit in a complete weighted graph is often called Travelling problem or nearest neighbour algorithm.(vogel approxim.)
48. What is a coincidence matrix? Describe it. Tableau (matrix) = rewrites graph into the matrix, example: when doing shortest path problem, I can draw it like a graph or write it as a matrix – it is the same
49. What is weighted graph? What is the meaning of the weights in the maximal flow problem? Ohodnoceny graf, graph with values, and each plumb´s value means maximal flow trough this plumb from a to b
8 Network models
50.What are the differences between the transportation problem and assignment problem?
the transportation problem: deals with the distribution of goods from several points of supply(sources) to a number of points of demand(destinations).
Capacities (suppliers or sources),requirements are customers, destinations and demands. Demands have requirements and suppliers have capacities and I have to divide it so everybody is satisfied.
Models can also be used when a firm is trying to decide where to locate a new facility.
Good financial decisions concerning facility location also attempt to minimize total transportation and production costs for the entire system, I have requirements of demand
assignment problem: refers to the class of LP problems that involves determining the most efficient assignment of: people to projects, sales people to territories, jobs to machines etc. the objective is most often to minimize total costs or total time of performing the tasks at hand.
One important characteristic of as. problem is that only one job or worker is assigned to one machine or project. Capacitiy, requirements = 1 – always offering 1 and I want 1
51.What is total opportunity cost matrix? In which method it is used? How does it look?
When we have at least one zero in every row and column=zero opportunity cells more competent for assignment. In Vogel´s approximation method.
Jobs x y z
A 0 1 2
B 6 0 3
C 5 4 0