State whether the following statement is True or False: The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost - Mathematics and Statistics

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True or False

State whether the following statement is True or False:

The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost

Options

  • True

  • False

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Solution

False

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Chapter 2.7: Assignment Problem and Sequencing - Q.3

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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
C 3 4 6 1
D 4 15 4 9

 


Determine `l_92 and l_93, "given that"  l_91 = 97, d_91 = 38 and q_92 = 27/59`


Solve the following minimal assignment problem and hence find minimum time where  '- ' indicates that job cannot be assigned to the machine : 

Machines Processing time in hours
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

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 departmental head has three jobs and four subordinates. The subordinates differ in their capabilities and the jobs differ in their work
contents. With the help of the performance matrix given below, find out which of the four subordinates should be assigned which jobs ?

Subordinates Jobs
I II III
A 7 3 5
B 2 7 4
C 6 5 3
D 3 4 7

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 3 2 4 4 5
4 18 9 12 17 15
5 11 6 14 19 10

Five different machines can do any of the five required jobs, with different profits resulting from each assignment as shown below:

Job Machines (Profit in ₹)
A B C D E
1 30 37 40 28 40
2 40 24 27 21 36
3 40 32 33 30 35
4 25 38 40 36 36
5 29 62 41 34 39

Find the optimal assignment schedule.


The assignment problem is said to be unbalance if ______


The assignment problem is said to be balanced if ______.


Choose the correct alternative :

The assignment problem is said to be balanced if it is a ______.


Choose the correct alternative :

In an assignment problem if number of rows is greater than number of columns then


Fill in the blank :

An _______ is a special type of linear programming problem.


In an assignment problem, if number of column is greater than number of rows, then a dummy column is added.


State whether the following is True or False :

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


State whether the following is True or False :

It is not necessary to express an assignment problem into n x n matrix.


Solve the following problem :

A dairy plant has five milk tankers, I, II, III, IV and V. These 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 130 100 145 160 175
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?


Choose the correct alternative:

The assignment problem is generally defined as a problem of ______


Choose the correct alternative: 

Assignment Problem is special case of ______


Choose the correct alternative:

When an assignment problem has more than one solution, then it is ______


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


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


State whether the following statement is True or False:

In assignment problem, if number of columns is greater than number of rows, then a dummy row is added


State whether the following statement is True or False: 

In assignment problem each worker or machine is assigned only one job


What is the Assignment problem?


Give mathematical form of Assignment problem


A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.

  Programmers
    P Q R
Programmers 1 120 100 80
  2 80 90 110
  3 110 140 120

Assign the programmers to the programme in such a way that the total computer time is least.


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:

Number of basic allocation in any row or column in an assignment problem can be


Choose the correct alternative:

The purpose of a dummy row or column in an assignment problem is to


Choose the correct alternative:

In an assignment problem involving four workers and three jobs, total number of assignments possible are


A car hire company has one car at each of five depots a, b, c, d and e. A customer in each of the fine towers A, B, C, D and E requires a car. The distance (in miles) between the depots (origins) and the towers(destinations) where the customers are given in the following distance matrix.

  a b c d e
A 160 130 175 190 200
B 135 120 130 160 175
C 140 110 155 170 185
D 50 50 80 80 110
E 55 35 70 80 105

How should the cars be assigned to the customers so as to minimize the distance travelled?


A natural truck-rental service has a surplus of one truck in each of the cities 1, 2, 3, 4, 5 and 6 and a deficit of one truck in each of the cities 7, 8, 9, 10, 11 and 12. The distance(in kilometers) between the cities with a surplus and the cities with a deficit are displayed below:

    To
    7 8 9 10 11 12
From 1 31 62 29 42 15 41
2 12 19 39 55 71 40
3 17 29 50 41 22 22
4 35 40 38 42 27 33
5 19 30 29 16 20 33
6 72 30 30 50 41 20

How should the truck be dispersed so as to minimize the total distance travelled?


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

A job production unit has four jobs P, Q, R, 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

Complete the following activity to find the optimal assignment to minimize the total processing cost.

Solution:

Step 1: Subtract the smallest element in each row from every element of it. New assignment matrix is obtained as follows :

Job Machines
(Processing cost in ₹)
I II III IV
P 6 0 8 4
Q 4 3 2 0
R 0 2 4 5
S 4 2 0 6

Step 2: Subtract the smallest element in each column from every element of it. New assignment matrix is obtained as above, because each column in it contains one zero.

Step 3: Draw minimum number of vertical and horizontal lines to cover all zeros:

Job Machines
(Processing cost in ₹)
I II III IV
P 6 0 8 4
Q 4 3 2 0
R 0 2 4 5
S 4 2 0 6

Step 4: From step 3, as the minimum number of straight lines required to cover all zeros in the assignment matrix equals the number of rows/columns. Optimal solution has reached.

Examine the rows one by one starting with the first row with exactly one zero is found. Mark the zero by enclosing it in (`square`), indicating assignment of the job. Cross all the zeros in the same column. This step is shown in the following table :

Job Machines
(Processing cost in ₹)
I II III IV
P 6 0 8 4
Q 4 3 2 0
R 0 2 4 5
S 4 2 0 6

Step 5: It is observed that all the zeros are assigned and each row and each column contains exactly one assignment. Hence, the optimal (minimum) assignment schedule is :

Job Machine Min.cost
P II `square`
Q `square` 21
R I `square`
S III 34

Hence, total (minimum) processing cost = 25 + 21 + 19 + 34 = ₹`square`


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