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प्रश्न
What is the Assignment problem?
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उत्तर
Suppose that we have ‘m1 jobs to be performed on ‘n’ machines.
The cost of assigning each job to each machine is Cij (i = 1, 2, … n and j = 1, 2, … , n).
Our objective is to assign the different jobs to the different machines (one job per machine) to minimize the overall cost.
This is known as assignment problem.
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संबंधित प्रश्न
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 |
Determine `l_92 and l_93, "given that" l_91 = 97, d_91 = 38 and q_92 = 27/59`
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.
The assignment problem is said to be balanced if ______.
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.
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
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?
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 |
