OPERATIONS RESEARCH - OR Paper 2

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OPERATIONS RESEARCH 6/7th Semester ME 311 (MAY 2005)
I

1. What are the main characteristics of operations research?
2. Define a feasible region.
3. When does simplex method indicate that the LPP has unbounded solution?
4. What do you mean by degeneracy in transportation problem?
5. What is Dynamic Programming?
6. Define a Critical Activity.
7. Distinguish between PERT and CPM
8. Define a Queue
9. Solve the game whose pay-off matrix is

Fig. 1

Player B

B1 B2 B3

(These Figures are Not Available)

1. Write the dual of the following problem:

Maximize z=20x1 + 40x2
Subject to 2x1 + 20x2 =40
20x1 + 3x2 =20
4x1 + 15x2 =30
x1, x2 ≥ 0
II Use two-phase Simplex method to
Maximize z=5x1 - 4x2 +3 x3
Subject to 2x1 + x2 - 6x3 =20
6x1 + 5x2 +10 x3≤ 76
8x1 -3x2 + 6 x3≤ 50 and x1, x2 x3, ≥ 0
III Find the optimum solution to the following transportation problem:

Fig. 2

Factory	Warehouse				Capacity
	D	E	F	G
A	42	48	38	37	160
B	40	49	52	51	150
C	39	38	40	43	190
Demand	80	90	116	160

IV At a central warehouse, vehicles arrive at the rate of 18 per hour and arrival rate follows Poisson distribution. The unloading time of the vehicle follows exponential distribution and he unloading rate is 6 vehicles per hour. There are 4 unloading crews. Find the following:

1. Probability of having zero vehicles
2. Average number of vehicles waiting in the queue and in the system.
3. Average waiting time of the vehicles in queue and in the system.

V The annual demand for a component is 7200 units. The carrying cost is Rs. 500/ unit/ year, the ordering cost is Rs. 1500 per order and the shortage cost is Rs. 2000/ unit / year. Find the optimum value of:

1. Economic order quantity
2. Maximum inventory
3. Maximum shortage quantity
4. Inventory period
5. Cycle time.

VI Solve the following sequencing problem, giving an optimal solution when passing is not allowed. What is the total elapsed time?

Fig. 3

Machine	Processing Time in Hours
Job	M1	M2	M3	M4
1	20	3	3	25
2	12	5	1	11
3	18	4	2	10
4	17	2	4	28

VII With the help of the information given in the table below, find out the critical path, earliest start and finish time, latest start and finish time of each event. Also calculate the total slack of each activity.

Fig. 4

Activity	Duration	Immediate Predecessor
1-2	6	-
1-3	8	-
2-3	3	1-2
3-4	4	1-3,2-3
3-6	12	1-3,2-3
3-5	10	1-3,2-3
2-4	8	1-2
4-6	8	2-4,3-4
5-6	6	3-5
5-7	12	3-5
6-7	8	4-6,3-6,5-6
7-8	7	6-7,5-7

VIII The data for the project is given below:

Fig. 5

Activity	Preceding Activity	Time (weeks)			Cost (Rs)
		Normal		Crash	Normal		Crash
A	-	3	2		18000	19000
B	-	8	6		600	1000
C	B	6	4		10000	12000
D	B	5	2		4000	10000
E	A	13	10		3000	9000
F	A	4	4		15000	15000
G	F	2	1		1200	1400
H	C,E,G	6	4		3500	4500
I	F	2	1		7000	8000

1. Draw the network diagram and find the critical path.
2. If a dead line of 17 weeks is imposed for completion of he project, what activities will be crashed, what would be he additional cost, and what would be he critical activities o the network of the crashing?

IX A company is dealing with newly invested telephone device is faced with the problem of the following strategies:

1. manufacture the device itself
2. to be paid on royalty basis by another manufacturer
3. sell the rights for its invention for a lumpsum.

The profit in thousand of rupees that can be expected in each case and the associated probabilities with the sales volume is shown in table:

Fig. 6

Event	Probability	Manufacture Itself	Royalties	Sell the rights
High demand	0.2	100	40	20
Medium demand	0.3	30	25	20
Low demand	0.5	-10	15	20

1. Represent the company’s problem in the form of a decision tree.
2. Extend the diagram further for the following information:
3. If the company manufactures itself and the sales are medium and high, it has he opportunity of developing a new version of its telephone.

(ii) Past experience says there is 60% chance of successful development.
(iii) If the cost of development is Rs. 20 and the profits are Rs. 35 and Rs. 10 for high and medium demand respectively.
All monetary values are in thousands.