English
Maharashtra State BoardHSC Commerce (English Medium) 12th Standard Board Exam
Question Papers286
Textbook Solutions12946
MCQ Online Mock Tests99
Important Solutions6950
Concept Notes & Videos335
Time Tables34
Syllabus

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

Advertisements
Advertisements

Question

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

MCQ
True or False
Advertisements

Solution

False

shaalaa.com
Assignment Problem
  Is there an error in this question or solution?
Q 1
Chapter 2.7: Assignment Problem and Sequencing - Q.3

APPEARS IN

SCERT Maharashtra Mathematics and Statistics (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 2.7 Assignment Problem and Sequencing
Q.3 | Q 1

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Suggest optimum solution to the following assignment. Problem, also find the total minimum service time.
                                             Service Time ( in hrs.)

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

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.


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 balanced if ______.


Fill in the blank :

An _______ is a special type of linear programming problem.


State whether the following is True or False :

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


Solve the following problem :

A plant manager has four subordinates, and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. This estimate of the time each man would take to perform each task is given in the effectiveness matrix below.

  I II III IV
A 7 25 26 10
B 12 27 3 25
C 37 18 17 14
D 18 25 23 9

How should the tasks be allocated, one to a man, as to minimize the total man hours?


Choose the correct alternative: 

Assignment Problem is special case of ______


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


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


What is the Assignment problem?


Give mathematical form of Assignment problem


Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below. Determine the allocation that minimizes the overall processing cost.

    Machine
    U V W
Jobs A 17 25 31
B 10 25 16
C 12 14 11

(cost is in ₹ per unit)


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:

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


Choose the correct alternative:

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


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

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`


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.


Share
Notifications

Englishहिंदीमराठी
Login
Create free account


      Forgot password?
Course
Use app×