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State whether the following is True or False :
The purpose of dummy row or column in an assignment problem is to obtain balance between total number of activities and total number of resources.
Options
True
False
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Solution
The purpose of dummy row or column in an assignment problem is to obtain balance between total number of activities and total number of resources True.
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RELATED QUESTIONS
Four new machines M_{1}, M_{2}, M_{3} and M_{4} are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M_{2} cannot be placed at C and M_{3} cannot be placed at A. The cost matrix is given below.
Machines | Places | ||||
A | B | C | D | E | |
M_{1} | 4 | 6 | 10 | 5 | 6 |
M_{2} | 7 | 4 | – | 5 | 4 |
M_{3} | – | 6 | 9 | 6 | 2 |
M_{4} | 9 | 3 | 7 | 2 | 3 |
Find the optimal assignment schedule
In the modification of a plant layout of a factory four new machines M_{1}, M_{2}, M_{3} and M_{4} are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M_{2} cannot be placed at C and M_{3} cannot be placed at A. The cost of locating a machine at a place (in hundred rupees) is as follows.
Machines | Location | ||||
A | B | C | D | E | |
M_{1} | 9 | 11 | 15 | 10 | 11 |
M_{2} | 12 | 9 | – | 10 | 9 |
M_{3} | – | 11 | 14 | 11 | 7 |
M_{4} | 14 | 8 | 12 | 7 | 8 |
Find the optimal assignment schedule.
Fill in the blank :
An assignment problem is said to be unbalanced when _______.
Fill in the blank :
When the number of rows is equal to the number of columns then the problem is said to be _______ assignment problem.
Fill in the blank :
If the given matrix is not a _______ matrix, the assignment problem is called an unbalanced problem.
Fill in the blank :
In an assignment problem, a solution having _______ total cost is an optimum solution.
To convert the assignment problem into a maximization problem, the smallest element in the matrix is deducted from all other elements.
State whether the following is True or False
In number of lines (horizontal on vertical) > order of matrix then we get optimal solution.
Solve the following problem :
Solve the following assignment problem to maximize sales:
Salesman | Territories | ||||
I | II | III | IV | V | |
A | 11 | 16 | 18 | 15 | 15 |
B | 7 | 19 | 11 | 13 | 17 |
C | 9 | 6 | 14 | 14 | 7 |
D | 13 | 12 | 17 | 11 | 13 |
Choose the correct alternative:
The cost matrix of an unbalanced assignment problem is not a ______
An unbalanced assignment problems can be balanced by adding dummy rows or columns with ______ cost
A ______ assignment problem does not allow some worker(s) to be assign to some job(s)
State whether the following statement is True or False:
To convert the assignment problem into maximization problem, the smallest element in the matrix is to deducted from all other elements
Find the assignments of salesman to various district which will yield maximum profit
Salesman | District | |||
1 | 2 | 3 | 4 | |
A | 16 | 10 | 12 | 11 |
B | 12 | 13 | 15 | 15 |
C | 15 | 15 | 11 | 14 |
D | 13 | 14 | 14 | 15 |
For the following assignment problem minimize total man hours:
Subordinates | Required hours for task | |||
I | II | III | IV | |
A | 7 | 25 | 26 | 10 |
B | 12 | 27 | 3 | 25 |
C | 37 | 18 | 17 | 14 |
D | 18 | 25 | 23 | 9 |
Subtract the `square` element of each `square` from every element of that `square`
Subordinates | Required hours for task | |||
I | II | III | IV | |
A | 0 | 18 | 19 | 3 |
B | 9 | 24 | 0 | 22 |
C | 23 | 4 | 3 | 0 |
D | 9 | 16 | 14 | 0 |
Subtract the smallest element in each column from `square` of that column.
Subordinates | Required hours for task | |||
I | II | III | IV | |
A | `square` | `square` | 19 | `square` |
B | `square` | `square` | 0 | `square` |
C | `square` | `square` | 3 | `square` |
D | `square` | `square` | 14 | `square` |
The lines covering all zeros is `square` to the order of matrix `square`
The assignment is made as follows:
Subordinates | Required hours for task | |||
I | II | III | IV | |
A | 0 | 14 | 19 | 3 |
B | 9 | 20 | 0 | 22 |
C | 23 | 0 | 3 | 0 |
D | 9 | 12 | 14 | 0 |
Optimum solution is shown as follows:
A → `square, square` → III, C → `square, square` → IV
Minimum hours required is `square` hours
State whether the following statement is true or false:
To convert a maximization-type assignment problem into a minimization problem, the smallest element in the matrix is deducted from all elements of the matrix.
To solve the problem of maximization objective, all the elements in the matrix are subtracted from the largest element in the matrix.
Three new machines M1, M2, M3 are to be installed in a machine shop. There are four vacant places A, B, C, D. Due to limited space, machine M2 can not be placed at B. The cost matrix (in hundred rupees) is as follows:
Machines | Places | |||
A | B | C | D | |
M_{1} | 13 | 10 | 12 | 11 |
M_{2} | 15 | - | 13 | 20 |
M_{3} | 5 | 7 | 10 | 6 |
Determine the optimum assignment schedule and find the minimum cost.