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State whether the following statement is True or False:
In assignment problem each worker or machine is assigned only one job
Options
True
False
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Solution
True
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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 
Solve the following minimal assignment problem :
Machines  A  B  C  D  E 
M_{1}  27  18  ∞  20  21 
M_{2}  31  24  21  12  17 
M_{3}  20  17  20  ∞  16 
M_{4}  21  28  20  16  27 
Determine `l_92 and l_93, "given that" l_91 = 97, d_91 = 38 and q_92 = 27/59`
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 
In a factory there are six jobs to be performed each of which should go through two machines A and B in the order A  B. The processing timing (in hours) for the jobs arc given here. You are required to determine the sequence for performing the jobs that would minimize the total elapsed time T. What is the value of T? Also find the idle time for machines · A and B.
Jobs  J_{1}  J_{2}  J_{3}  J_{4}  J_{5}  J_{6} 
Machine A  1  3  8  5  6  3 
MAchine B  5  6  3  2  2  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
The objective of an assignment problem is to assign ______.
Fill in the blank :
When an assignment problem has more than one solution, then it is _______ optimal solution.
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:
The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost
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
What is the difference between Assignment Problem and Transportation 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 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?
Choose the correct alternative:
Number of basic allocation in any row or column in an assignment problem can be
Choose the correct alternative:
If number of sources is not equal to number of destinations, the assignment problem is called ______
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 truckrental 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`
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.