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प्रश्न
To convert the assignment problem into a maximization problem, the smallest element in the matrix is deducted from all other elements.
पर्याय
True
False
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उत्तर
This statement is False.
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संबंधित प्रश्न
In the modification of a plant layout of a factory four new machines M1, M2, M3 and M4 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 M2 cannot be placed at C and M3 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 | |
| M1 | 9 | 11 | 15 | 10 | 11 |
| M2 | 12 | 9 | – | 10 | 9 |
| M3 | – | 11 | 14 | 11 | 7 |
| M4 | 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.
Maximization assignment problem is transformed to minimization problem by subtracting each entry in the table from the _______ value in the table.
Fill in the blank :
In an assignment problem, a solution having _______ total cost is an optimum solution.
Fill in the blank :
In maximization type, all the elements in the matrix are subtracted from the _______ element in the matrix.
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 |
Solve the following problem :
The estimated sales (tons) per month in four different cities by five different managers are given below:
| Manager | Cities | |||
| P | Q | R | S | |
| I | 34 | 36 | 33 | 35 |
| II | 33 | 35 | 31 | 33 |
| III | 37 | 39 | 35 | 35 |
| IV | 36 | 36 | 34 | 34 |
| V | 35 | 36 | 35 | 33 |
Find out the assignment of managers to cities in order to maximize sales.
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)
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.
