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:

1. Obtain an initial basic feasible solution using VAM
2. 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:

1. Find an initial feasible solution using VAM
2. 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:

1. Find initial feasible solution using VAM
2. 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