- A factory has five jobs A, B, C, D and E to be done by 5 workers 1,2,3,4 and 5. Each worker is assigned one job. The number of hours each worker would take to complete each job is given in the following table.
| Workers | Job | ||||
| A | B | C | D | E | |
| 1
2 3 4 5 |
55
52 36 54 58 |
54
48 40 60 62 |
48
46 44 50 56 |
70
64 60 48 80 |
76
78 64 54 72 |
Find the assignment of jobs to workers in such a way that the total time taken to perform all the jobs is minimum.
2. A construction project work consists of four major jobs for which four contractors have submitted tenders. The tender amounts quoted in thousands of rupees are given in the matrix as:
| Contractors | Jobs | |||
| J1 | J2 | J3 | J4 | |
| C1
C2 C3 C4 |
29
42 34 28 |
58
54 50 62 |
70
66 74 78 |
40
34 30 42 |
Find the assignment which minimizes total cost of the project. Each contractor has to be assigned one job.
- A School is taking bids on the City’s four school bus routes. Four transporters have submitted the bids as given in the following table:
| Company | Bids | |||
| Route1 | Route2 | Route3 | Route4 | |
| Company1
Company2 Company3 Company4 |
Rs. 8,500
— Rs. 6,000 — |
Rs. 10,000
Rs. 8,000 — — |
—
— Rs. 4,000 Rs. 8,000 |
—
Rs. 8,000 — Rs. 10,000 |
Suppose each bidder can be assigned only one route. Use the assignment model to minimize the school’s cost running the four bus routes.
- The municipal corporation of a city has decided to carry out road repairs in four main areas of the city. The estimated cost of the project is Rs. 100 lakhs. If necessary, then a supplementary provision of funds will also be made. The corporation has invited tenders and 5 contractors have sent in their bids. One road will be awarded to only one contractor.
(a) Find the best way of assigning the repair work to the contractors and the costs.
(b) If it is necessary to seek supplementary grants, then what should be the amount sought?
(c) Which of the five contractors will be unsuccessful in his bid?
| Contractors | Roads | |||
| R1 | R2 | R3 | R4 | |
| C1
C2 C3 C4 C5 |
17
14 18 20 20 |
28
34 36 24 30 |
38
40 42 36 42 |
30
38 36 38 32 |
- In a plant layout of a factory four new machines M1, M2, M3, and M4 are to be installed in a machine shop. There are five vacant places A, B, C, D, and E available. Because of limited space machine M2 cannot be placed at C and M3 cannot be placed at A. The cost of locating of machines in various places is given below (in Rs. ’00). Find optimum assignment schedule.
| A | B | C | D | E | |
| M1
M2 M3 M4 |
17
24 – 28 |
22
18 22 16 |
30
– 28 24 |
20
20 22 14 |
22
18 14 16 |
- A firm employs typists for job-work on an hourly basis. There are five typists available and their charges and speeds are different. Only one job is given to one typist and a typist is paid for full hour even if he/she works for a fraction of an hour. Find the least cost allocation for the following data:
| Â Â Â Â Â Â Â Â Â Â Â Typist | Rate per hour
(Rs) |
No. of pages Typed
Per hour |
Job | No. of pages |
| A
B C D E |
5
6 3 4 4 |
12
14 8 10 11 |
P
Q R S T |
200
176 150 300 240 |
- ABC Ltd. has rented a new office. There are five cabins (001, 002, 003, 004 & 005) in the office which are to be assigned to five managers. Each cabin has its own pros and cons. Each of the five managers was asked to rank the preferences amongst the cabins. Their preferences were recorded in a table as indicated below:-
| Room
Preference |
Manager | ||||
| M1 | M2 | M3 | M4 | M5 | |
| 001
003 004 |
002
004 005 001 |
003
001 004 005 002 |
002
005 004 003 |
001
002 004 |
|
Most of the manager did not list all the five cabins since they were not satisfied with some of these. Assuming that their preferences can be quantified by numbers, find out as to which manager should be assigned to which cabin, so that their satisfaction level is highest.
- XYZ Corporation has four plants each of which can manufacture any one of four products. The production costs differ from one plant to another as do sales revenue. Given the revenue and cost data below, obtain which product each plant should produce to maximize the profit.
|
Plant |
Sales Revenue (Rs. ‘000) | Cost (Rs. ‘000) | ||||||
| Product | Product | |||||||
| 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | |
| A
B C D |
52
60 55 58 |
68
70 67 65 |
49
51 53 54 |
62
74 70 69 |
49
49 52 55 |
60
63 62 64 |
45
45 49 48 |
61
69 68 66 |
- A five star hotel has four banquet halls. Four parties approached to reserve a hall on the same day. They were told that first choice among the four halls would cost Rs. 10,000/-. They were told to indicate 2nd, 3rd & 4th preferences and the price they would be willing to pay for these choices. Two parties A and D told they were not interested in hall no. 3 and 4.
Following table shows preference wise income details. Find optimal assignment. (Fig. in thousands)
| Halls | ||||
| Parties | 1 | 2 | 3 | 4 |
| A | 9 | 9 | – | – |
| B | 8 | 10 | 8 | 5 |
| C | 7 | 10 | 6 | 8 |
| D | 10 | 8 | – | – |
- A college Head of department has to provide teachers to all courses offered by his department for imparting highest possible quality education. There are 4 teachers and 4 courses. After detailed analysis, he has arrived at following ratings for each teacher & course combination.
| Course 1 | Course 2 | Course 3 | Course 4 | |
| Professor 1 | 70 | 40 | 60 | 70 |
| Professor 2 | 20 | 60 | 50 | 70 |
| Professor 3 | 20 | 30 | 40 | 60 |
| Professor 4 | 30 | 10 | 30 | 40 |
How to assign teachers to optimize educational quality?
- A company has 4 machines to do 3 jobs. Each job can be assigned to only one machine. The cost of each job machine combination is given in the table in Rs.
| M1 | M2 | M3 | M4 | |
| A | 9 | 12 | 14 | 19 |
| B | 4 | 6 | 8 | 9 |
| C | 5 | 7 | 9 | 11 |
A} Find optimal assignment which will minimize total production cost.
B} Is there any alternate optimal solution?   Is it possible to assign Job B to machine
M2 or M3 while maintaining same minimum cost?
C} Does any machine remain idle?
Source:- Vipin Saboo Tutorials
For any further clarifications, please feel free to contact Prof Vipin Saboo on 9820779873
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