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Question
Fill in the blank :
A dummy row(s) or column(s) with the cost elements as _______ is added to the matrix of an unbalanced assignment problem to convert into a square matrix.
Solution
A dummy row(s) or column(s) with the cost elements as zero is added to the matrix of an unbalanced assignment problem to convert into a square matrix.
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RELATED QUESTIONS
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 matrix is given below.
| Machines | Places | ||||
| A | B | C | D | E | |
| M1 | 4 | 6 | 10 | 5 | 6 |
| M2 | 7 | 4 | – | 5 | 4 |
| M3 | – | 6 | 9 | 6 | 2 |
| M4 | 9 | 3 | 7 | 2 | 3 |
Find the optimal assignment schedule
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.
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.
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.
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
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
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.
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 | |
| M1 | 13 | 10 | 12 | 11 |
| M2 | 15 | - | 13 | 20 |
| M3 | 5 | 7 | 10 | 6 |
Determine the optimum assignment schedule and find the minimum cost.
