- •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?
11. Which are the main types of the variables in the mathematical model?
Decision Variables are under the control of the decision-maker, the parameters, are beyond (mimo) the control of the decision-maker and are imposed by the external environment.
Parameters:
Exogenous Variables (external) are factor controlled from outside (economic conditions, actions of competitors (konkurence), prices of raw materials).
Policies and Constraints A decision-maker often operates within constraints imposed by company policy, legal restraints, or physical limitations.
Performance Measures (výkon) Managers always have objectives or goals that they are trying to achieve.
Intermediate Variables They are used to relate the decision variables and exogenous variables to the performance measures.
11. Describe the process of formulation and application of the linear programming model.
A. Formulating the model. a) Selection of a Time Horizonb) Selection of Decision Variables and Parameters
c) Definition of the Constraints d) Selection of the Objective Function:
Maximize total production, in units, Minimize production time, Maximize share of market for all or some products, Maximize total sales, in dollars or units, Minimize changes of production pattern, Minimize the use of a particular scarce (or expensive) commodity.
B. Gathering the data. C. Obtaining an optimal solution. a) Calculations b) Computer software D. Applying sensitivity analysis. a) Data Uncertainty How the changes in the input data will influence the solution b) Dynamic Considerations Development in time c) Input Errors
E. Testing and implementing the solution. The solution should be tested fully to ensure that the model clearly represents the real situation. When testing is complete, the model can be implemented. Implementation usually means solving the model with real data
What is the goal of the linear programming model?
To find production levels that will produce the max profit or min cost, the model will clearly represent the real situation.
2 Introduction to linear programming
13. Describe the linear programming model (3 parts). 3 parts of model: a) Objective (target) function – a linear mathematical relationship describing an objective of the firm, in terms of decision variables – this function is to be maximized or minimized. The decision maker will use it to evaluate alternative solutions to the problem. b) Constrains (conditions) consist of variables, are in form of inequalities a) capacityc. (<=) b) requirement (<=) c) exact value (=) d) balance (compering variables to each other)
c)Nonnegativity constrains (every x >=0)
14. Describe the constraints and the objective function in the linear programming model.
objective function a linear mathematical relationship describing an objective of the firm, this function is to be maximized or minimized. The decision maker will use it to evaluate alternative solutions to the problem.
15.Which are the basic groups of applications of the linear programming model?
The shift pattern problem,The cutting problem, Transportation problem, travelling salesman problem, shortest path problem, optimization, maximum flow problem
16.Describe the shift pattern problem. The production manager wants to devise a shift pattern for his workforce, objective is to simply find a feasible schedule to satisfy all constraints, have the minimum work-force.
17. Describe the cutting problem. The goal of this is to cut product into required size with minimum waste and sell it with maximum profit (as much pieces as possible)