Quantitative Analysis for Decision Making MBA Assignment
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Give Answers to the Following Questions
1. A company has three production facilities P1, P2, and P3 with production capacities of 70, 80, and 180 units per week of a product respectively. These units are to be shipped to four warehouses W1, W2, W3, and W4 with requirement of 50, 60, 70, and 150 units per week respectively. The transportation cost (in birr) per unit between productions facilities to warehouses are given below:
To From | W1 | W2 | W3 | W4 | |||||
P1 | 10 | 30 | 50 | 10 | |||||
P2 | 40 | 30 | 40 | 60 | |||||
P3 | 32 | 8 | 70 | 20 | |||||
Worker |
Job (cost in ’00 Br.) | ||||||||
I | II | III |
Required: find the optimal solution using the final table of VAM?
2. Each jobs can be assigned to only one The cost of each job on each worker is given below:
Required: 1. Find the least cost allocation of the company?
To From | W1 | W2 | W3 | W4 | ||||||
P1 | 10 | 30 | 50 | 10 | ||||||
P2 | 40 | 30 | 40 | 60 | ||||||
P3 | 32 | 8 | 70 | 20 | ||||||
Worker |
Job (cost in ’00 Br.) | |||||||||
I | II | III | IV | V | ||||||
A | 25 | 18 | 32 | 20 | 21 | |||||
2. What is the total assignment cost of the company for this problem? Apply Hungarian method
3. A firm employs typists on hourly piece-rate basis for their daily work. There are five typists and their charges and speed are According to an earlier understanding only one job is given to one typist and the typist is paid for a full hour even if he/she works for a fraction of an hour. Find the least cost allocation and the total assignment cost of the company using both
To From | W1 | W2 | W3 | W4 | |||||||||||||||
P1 | 10 | 30 | 50 | 10 | |||||||||||||||
P2 | 40 | 30 | 40 | 60 | |||||||||||||||
P3 | 32 | 8 | 70 | 20 | |||||||||||||||
Worker |
Job (cost in ’00 Br.) | ||||||||||||||||||
I | II | III | IV | V | |||||||||||||||
A | 25 | 18 | 32 | 20 | 21 | ||||||||||||||
B | 25 | 25 | 21 | 12 | 17 | ||||||||||||||
To From | W1 | W2 | W3 | W4 | |||||||||||||||
P1 | 10 | 30 | 50 | 10 | |||||||||||||||
P2 | 40 | 30 | 40 | 60 | |||||||||||||||
P3 | 32 | 8 | 70 | 20 | |||||||||||||||
Worker |
Job (cost in ’00 Br.) | ||||||||||||||||||
I | II | III | IV | V | |||||||||||||||
A | 25 | 18 | 32 | 20 | 21 | ||||||||||||||
Enumeration and Hungarian method for the above data:
4. A car rental company has one car at each of five depots a, b, c, d and e. A customer in each of the five towns A, B, C, D and E requires a car. The distance in (in kilometers) between the depots and towns where the customers are, is given in the following distance matrix:
Depots
A | B | c | D | E | |
A | 160 | 130 | 175 | 190 | 200 |
B | 135 | 120 | 130 | 160 | 175 |
C | 140 | 110 | 155 | 170 | 185 |
D | 50 | 50 | 90 | 80 | 110 |
E | 55 | 35 | 70 | 80 | 105 |
How should the cars be assigned to the customers so as to minimize the distance traveled?
5. A cement factory manager is considering the best way to transport cement from his three manufacturing centers P, Q, R to depots A,B, C, D and The weekly production and demands along with transportation costs per tonne are given below.
A | B | C | D | E | Supply | |
P | 4 | 1 | 3 | 4 | 4 | 60 |
Q | 2 | 3 | 2 | 2 | 3 | 35 |
R | 3 | 5 | 2 | 4 | 4 | 40 |
Demand | 22 | 45 | 20 | 18 | 30 |
On the basis of the above information:
- Obtain an initial basic feasible solution using VAM
- Test its optimality using MODI method
6. Five different machines can do any of the five required jobs, with different profits resulting from each assignment as shown in the table below. Find the maximum profit possible through optimal assignment.
Machines | |||||
A | B | C | D | E |
Jobs |
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 |
7. Four factories (F1, F2, F3 and F4) supply the requirements of three warehouses (W1, W2, and W3). The availability at the factories, the requirements of three warehouses and the unit transportation costs are shown the following table:
Warehouses | Capacity | ||||
W1 | W2 | W3 | |||
Factory |
F1 | 10 | 8 | 9 | 15 |
F2 | 5 | 2 | 3 | 20 | |
F3 | 6 | 7 | 4 | 30 | |
F4 | 7 | 6 | 8 | 35 | |
Demand | 25 | 26 | 49 |
Required:
- Find an initial feasible solution using VAM
- Find the optimal solutions using MODI method
8. Given the following assignment problem and find the optimal assignment of operators over those jobs.
Jobs | ||||||
A | B | C | D | E | ||
Operators | 1 | 6 | 2 | 5 | 3 | 6 |
2 | 2 | 5 | 8 | 7 | 7 | |
3 | 7 | 8 | 6 | 9 | 8 |
4 | 6 | 2 | 3 | 4 | 5 | |
5 | 9 | 3 | 8 | 9 | 7 | |
6 | 4 | 7 | 4 | 6 | 8 |
9. The delivery cost, supply (W, X and Y) and demand (A, B and C) are given in the table below.
A | B | C | Supply | |
W | 8 | 16 | 16 | 152 |
X | 32 | 48 | 32 | 164 |
Y | 16 | 32 | 48 | 154 |
Demand | 144 | 204 | 82 |
Required:
- Find initial feasible solution using VAM
- Determine optimal solution using MODI method
10. A company has to assign five pilots (A, B, C, D and E) are available to five flight numbers (1, 2, 3, 4 and 5). Certain of the flights are unsuitable and have been marked by M as seen in the table below.
Suggest the optimal assignment.
Flight Number | ||||||
1 | 2 | 3 | 4 | 5 | ||
Pilots |
A | 2 | 8 | M | 5 | 6 |
B | 0 | 1 | 8 | 2 | 6 | |
C | 5 | 6 | 1 | 4 | M | |
D | 7 | 4 | 8 | 2 | 3 |
E | 5 | 4 | 0 | 6 | 7 |