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प्रश्न
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
पर्याय
True
False
उत्तर
False
APPEARS IN
संबंधित प्रश्न
A company has a team of four salesmen and there are four districts where the company wants to start its business. After taking into account the capabilities of salesmen and the nature of districts, the company estimates that the profit per day in rupees for each salesman in each district is as below:
| 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 |
Find the assignment of salesman to various districts which will yield maximum profit.
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.
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.
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 :
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.
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 :
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)
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.
A marketing manager has list of salesmen and territories. Considering the travelling cost of the salesmen and the nature of territory, the marketing manager estimates the total of cost per month (in thousand rupees) for each salesman in each territory. Suppose these amounts are as follows:
| 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 |
Find the assignment of salesman to territories that will result in minimum cost.
