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. - Mathematics and Statistics

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MCQ
True or False

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.

Concept: Special Cases of Assignment Problem
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Chapter 7: Assignment Problem and Sequencing - Miscellaneous Exercise 7 [Page 128]

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Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 7 Assignment Problem and Sequencing
Miscellaneous Exercise 7 | Q 3.09 | Page 128

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


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.


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
M1 13 10 12 11
M2 15 - 13 20
M3 5 7 10 6

Determine the optimum assignment schedule and find the minimum cost.


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