हिंदी

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

प्रश्न

विकल्प

True
False

MCQ

सत्य या असत्य

उत्तर

This statement is False.

Explanation:

In an assignment problem, if the number of rows is less than columns, a dummy row is added to make it a square matrix.
A dummy column is added only when rows exceed columns, not the other way around.

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Assignment Problem

क्या इस प्रश्न या उत्तर में कोई त्रुटि है?

Q 3.08 Q 3.07 Q 3.09

अध्याय 7: Assignment Problem and Sequencing - Miscellaneous Exercise 7 [पृष्ठ १२८]

APPEARS IN

बालभारती Mathematics and Statistics 2 (Commerce) [English] Standard 12 Maharashtra State Board

अध्याय 7 Assignment Problem and Sequencing
Miscellaneous Exercise 7 | Q 3.08 | पृष्ठ १२८

2022-2023 (March) Official (with solutions)

Q 4.B.iii | 1 mark

2023-2024 (July) Official (with solutions)

Q 4.B.iii | 1 mark

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Assignment Problem

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संबंधित प्रश्न

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
M₁	27	18	∞	20	21
M₂	31	24	21	12	17
M₃	20	17	20	∞	16
M₄	21	28	20	16	27

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
Machines	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)
Branch Manager	A	B	C	D
P	11	11	9	9
Q	13	16	11	10
R	12	17	13	8
S	16	14	16	12

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

The assignment problem is said to be unbalance if ______

Choose the correct alternative :

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

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?

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:

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

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

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.

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 ______

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 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 ₹)
Job	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 ₹)
Job	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 ₹)
Job	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 ₹)
Job	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 :