Fill in the blank : An assignment problem is said to be unbalanced when _______. - Mathematics and Statistics

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Fill in the Blanks

Fill in the blank :

An assignment problem is said to be unbalanced when _______.

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Solution

An assignment problem is said to be unbalanced when number of rows is not equal to the number of columns.

Concept: Special Cases of Assignment Problem
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Chapter 7: Assignment Problem and Sequencing - Miscellaneous Exercise 7 [Page 127]

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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 2.01 | Page 127

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.


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 :

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.


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 maximization type, all the elements in the matrix are subtracted from the _______ element in the matrix.


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.


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.


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.


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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