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In an assignment problem if number of rows is greater than number of columns, then dummy ______ is added - Mathematics and Statistics

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In an assignment problem if number of rows is greater than number of columns, then dummy ______ is added

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column

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Chapter 2.7: Assignment Problem and Sequencing - Q.2

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SCERT Maharashtra Mathematics and Statistics (Commerce) [English] 12 Standard HSC
Chapter 2.7 Assignment Problem and Sequencing
Q.2 | Q 4

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RELATED QUESTIONS

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job is given in the following table:

         Jobs

 

 

                          Machines

P

Q

R

S

                Processing Cost (Rs.)

 

A

31

25

33

29

B

25

24

23

21

C

19

21

23

24

D

38

36

34

40

 How should the jobs be assigned to the four machines so that the total processing cost is minimum?


Solve the following minimal assignment problem and hence find the minimum value : 

  I II III IV
A 2 10 9 7
B 13 2 12 2
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Suggest optimum solution to the following assignment. Problem, also find the total minimum service time.
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Counters Salesmen
A B C D
W 41 72 39 52
X 22 29 49 65
Y 27 39 60 51
Z 45 50 48 52

Solve the following minimal assignment problem : 

Machines A B C D E
M1 27 18 20 21
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Solve the following maximal assignment problem :

Branch Manager Monthly Business ( Rs. lakh)
A B C D
P 11 11 9 9
Q 13 16 11 10
R 12 17 13 8
S 16 14 16 12

 


A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job for each machine is given in the following table:

Jobs Machines
(Processing Cost in ₹)
P Q R S
A 31 25 33 29
B 25 24 23 21
C 19 21 23 24
D 38 36 34 40

Find the optimal assignment to minimize the total processing cost.


The assignment problem is said to be balanced if ______.


State whether the following is True or False :

In assignment problem, each facility is capable of performing each task.


Choose the correct alternative:

The assignment problem is generally defined as a problem of ______


Choose the correct alternative:

The assignment problem is said to be balanced if ______


If the given matrix is ______ matrix, the assignment problem is called balanced problem


What is the Assignment problem?


A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the time each man would take to perform each task is given below:

    Tasks
    1 2 3 4
Subordinates P 8 26 17 11
  Q 13 28 4 26
  R 38 19 18 15
  S 9 26 24 10

How should the tasks be allocated to subordinates so as to minimize the total manhours?


Find the optimal solution for the assignment problem with the following cost matrix.

    Area
    1 2 3 4
  P 11 17 8 16
Salesman Q 9 7 12 6
  R 13 16 15 12
  S 14 10 12 11

Choose the correct alternative:

North – West Corner refers to ______


Choose the correct alternative:

If number of sources is not equal to number of destinations, the assignment problem is called ______


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A dairy plant has five milk tankers, I, II, III, IV and V. Three milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.

  I II III IV V
A 150 120 175 180 200
B 125 110 120 150 165
C 130 100 145 160 170
D 40 40 70 70 100
E 45 25 60 70 95

How should the milk tankers be assigned to the chilling center so as to minimize the distance travelled?


A job production unit has four jobs P, Q, R, and S which can be manufactured on each of the four machines I, II, III, and IV. The processing cost of each job for each machine is given in the following table:

Job Machines
(Processing cost in ₹)
I II III IV
P 31 25 33 29
Q 25 24 23 21
R 19 21 23 24
S 38 36 34 40

Find the optimal assignment to minimize the total processing cost.


A department store has four workers to pack goods. The times (in minutes) required for each worker to complete the packings per item sold is given below. How should the manager of the store assign the jobs to the workers, so as to minimize the total time of packing?

Workers Packing of
  Books Toys Crockery Cutlery
A 3 11 10 8
B 13 2 12 12
C 3 4 6 1
D 4 15 4 9

Five wagons are available at stations 1, 2, 3, 4 and 5. These are required at 5 stations I, II, III, IV and V. The mileage between various stations are given in the table below. How should the wagons be transported so as to minimize the mileage covered?

  I II III IV V
1 10 5 9 18 11
2 13 9 6 12 14
3 7 2 4 4 5
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5 11 6 14 19 10

A plant manager has four subordinates and four tasks to perform. The subordinates differ in efficiency and task differ in their intrinsic difficulty. Estimates of the time subordinate would take to perform tasks are given in the following table:

  I II III IV
A 3 11 10 8
B 13 2 12 2
C 3 4 6 1
D 4 15 4 9

Complete the following activity to allocate tasks to subordinates to minimize total time.

Solution:

Step I: Subtract the smallest element of each row from every element of that row:

  I II III IV
A 0 8 7 5
B 11 0 10 0
C 2 3 5 0
D 0 11 0 5

Step II: Since all column minimums are zero, no need to subtract anything from columns.

Step III: Draw the minimum number of lines to cover all zeros.

  I II III IV
A 0 8 7 5
B 11 0 10 0
C 2 3 5 0
D 0 11 0 5

Since minimum number of lines = order of matrix, optimal solution has been reached

Optimal assignment is A →`square`  B →`square`

C →IV  D →`square`

Total minimum time = `square` hours.


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