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प्रश्न
The assignment problem is said to be balanced if ______.
पर्याय
Number of rows is greater than number of columns
Number of rows is lesser than number of columns
Number of rows is equal to number of columns
If the entry of row is zero
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उत्तर
The assignment problem is said to be balanced if number of rows is equal to number of columns.
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संबंधित प्रश्न
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 |
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 |
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 |
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 |
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 |
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.
Fill in the blank :
An _______ is a special type of linear programming problem.
State whether the following is True or False :
It is not necessary to express an assignment problem into n x n matrix.
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 ______
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
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)
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:
The purpose of a dummy row or column in an assignment problem is to
Choose the correct alternative:
The solution for an assignment problem is optimal if
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 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 |
