How can we assign the entering and departing variables?

Entering: The reduced profits are minus the coefficients of the non-basic variables in the Z-equation. MAX: the highest negative value. MIN: The highest positive value

Departing: Non-basic variables will become basic variables and vice versa

37. What is the goal of Gauss-Jordan elimination?

The goal of Gauss-Jordan elimination is to convert the matix into canomical form (identity matrix)

38. What contains the vector of basic optimal solution? Which are the values non-basic variables?

The contains the vector of basic optimal solution are basic variables and right-hand-side

Non-basic variables have “zero“ value

39. Interpret the shadow prices of the slack variables?

The sadow prices are the objective function coefficients for the slack (or surplus) variables at the optimal solution

40. Describe the proces of solution (steps )

-Obtaining an initial solution

- Checking an optimality criterion that indicates whether or not a termination condition has been met

- Improving the current solution

After an initial solution is found, the algorithm repetitively applies steps 2& 3

41. What is the number of basic and decision variables?

The constraint set is composed of (m+n-1) independent equations and acorrespoding nondegenerate basic solution will have exactly (m+n-1) basic variables.

42. Describe the optimality test of Transportation problé m? Which information it provides?

Use Northwest-corner method, lower cost entry method or Vogel’s approximation method by making successive improvements in initial basic feasible solution until no further decrease in transportation cos tis possible,

43. What is the purpose of Dantzing loops (closed path)

Starts and finishes at the field. With Dantzing loops, we can go to the left, down by 90 degree and turn back to the chosen cell and cant go up.

44. How do we solve the situation when the sum of sources is not equal to the sum of demands?

If supply > demand: Add dummy row in matrix with zero cost

If demand > supply: Add dummy column in matrix with zero cost

45. Descrive Vogel’s algorithm. Where i tis applied?

-For each row of the table identify the lowest and the next lowest cost cell. Leaving an origin or entering a destination

- This difference indicates where departure for the lowest-cost allocations will bring the highest increase in cost.

- Therefore, one assigns the maximum possible amount to that are that has the lowest cost in that row or column having the greatest cost different.

- If this assignment exhausts the demand at that destination, the corresponding column is eliminated for further consideration; similarly, if the assignment exhausts the supply at that origin, the corresponding row is eliminated. In either case, the origin and destination cost differences are recomputed, & the procedure continues in the same way.

*) I tis applied to find optimal solution of transportation problé m.

47. How do we solve with degeneration?

One simply assigns a close to zero value to a all in either row or column to be simultaneously eliminated and treat that variable in the remaining computation proces

48. Describe the graph call network?

• Connected graph, free of circuits. – Weighted with positive weights had exactly one starting point and 1 final point. A network model consists of nodes connected by arcs.

49. Describe the graph called spanning tree?

Subgraph of a tree tyoe with minimu m sum of arc weights

50. Describe the graph called Hamiltonian circuit. In which method i tis applied>

- Circuit through all arcs. I tis applied in Travelling Salesman Method

51. Describe the coincidence matrix

Had methods for comparing 2 classifications. Both must contain exactly the same items in the same order

52. What is weighted graph? What is the meaning of weights in the maximum flow problé m?

Weighted grap is assigned to every nodes

53. What are the differrences between transportation problé m and assignment problé m?

Transportation Problem: The objective is to minimize the cost of distribution a product for a number of sources or origins to a number of destinations in such a manner that the cost of transportation is minimum

Assignment Problem: Finds many allocation in allocation and scheduling

54. What is total opportunity cost matrix. In which method i this used?

-Opportunity cost is the cost of possible opportunity which is using in assignment problé m. We have at least one zero in every row and column = zero opportunity cells more competent for assignment.

I this used in Hungarian method

55. What is the goal of assignment problé m? What are the prerequisites?

- The goal is to find an optimal assignment of agents to task without once and ensuring that all tasks are completed

Prerequesites: are programming experience and solid programming skills, advanced background in linear optimization.

56. Goal of TSM: To find a simple cycle containing all nodes and minimizing the total distance

57. How can be applied the Vogel’s approximation for TSM?

-Calculate the different between the two lowest-cost are leaving an origin or entering a destination

- Choose the field that had the lowest cost in that row or column (having the greatest cost different)

-Delete all the other connections lines and column of the chosen field.

-Delete the connections which closes the circle before all places are included

58. Describe max flow and its solution?

-Finiding a path of positive capacity P from the sources to the sink, be a saturating path

-Reduce all capacities along the path, by the value of P

- Repeat the entire proces until no path of positive capacity exists from the source to the sink.

* Describe: The max flow problé m passing from the source to the sink is equal to the minimum capacity that, when removed in a specific way from the network, causes the situation that no flow can pass from the source to the sink.

59. Describe the shortest path problé m and its solution

The goal is to find a path through the network and from a particular origin (source) to a particular destination (sink) that has the shortest total distance

· We can use Dijstra’s algorithm as its solution

60. Describe Dijstra’s algorithm

- Set the distance fro the source node to zero and set all other nodes to infinity

- Mark all nodes as unvisited. Set the source node as a current one

- COnsider all its unvisited neighbors and compute their distance from source node

- Choose the unvisited node whose distance is shortest, and set it to a current node. Mark the previous current node is visited. A visited node not will be checked anymore

- If all nodes have been visited, the proces is finished. Otherwise repeat from step 3

61. What is a project? What are the main parts of the project?

It's a temporary endeavor undertaken to create a unique product, service or result. 1 Scope Management 2 Scheduling 3 Resource Management 4 Budgeting and Cost Management

 

62. What is the critical task in the project?

critical tasks are the jobs your team must complete to finish a project.

 

63. Describe the graph used in the critical path method.

Task Code, Task Name, Task Duration, Predcessor

48. Describe the graph call network?

• Connected graph, free of circuits. – Weighted with positive weights had exactly one starting point and 1 final point. A network model consists of nodes connected by arcs.

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