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Question
State whether the following is True or False :
It is not necessary to express an assignment problem into n x n matrix.
Options
True
False
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Solution
It is not necessary to express an assignment problem into n x n matrix False.
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RELATED QUESTIONS
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 |
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 ______
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.
In an assignment problem, if number of column is greater than number of rows, then a dummy column is added.
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?
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
State whether the following statement is True or False:
In assignment problem each worker or machine is assigned only one job
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?
Assign four trucks 1, 2, 3 and 4 to vacant spaces A, B, C, D, E and F so that distance travelled is minimized. The matrix below shows the distance.
| 1 | 2 | 3 | 4 | |
| A | 4 | 7 | 3 | 7 |
| B | 8 | 2 | 5 | 5 |
| C | 4 | 9 | 6 | 9 |
| D | 7 | 5 | 4 | 8 |
| E | 6 | 3 | 5 | 4 |
| F | 6 | 8 | 7 | 3 |
Choose the correct alternative:
If number of sources is not equal to number of destinations, the assignment problem is called ______
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The solution for an assignment problem is optimal if
Choose the correct alternative:
In an assignment problem involving four workers and three jobs, total number of assignments possible are
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 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 |
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.
