OPERATIONS RESEARCH - OR Paper 1 interview-questions

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OPERATIONS RESEARCH 6th Semester IT 210 (MAY 2005)
I (a) What is the condition that a set of m linear equations with n variable Ax = b be consistent?
(b) What is the necessary and sufficient condition for a solution set of a linearly independent set of equations to be a basic solution?
(c) What are the slack and surplus variable?
(d) Define symmetric primal and dual? (e) Define an assignment problem
(f) How can we solve a maximization assignment problem?
(g) What do you understand by sensitivity analysis?
(h) Define a symmetric game. Why is it called so?
(i) What is the probability of the queue being non-empty?
(j) If the primal problem has no feasible solution, then the dual will also have no feasible solution. Explain
II What do you mean by consistent solutions? Under what condition a set of linear equations will be consistent? Prove that a set of linearly independent set of equations are consistent but the converse is not necessarily true. Define a basic solution of a system of m independent linear equations with n unknowns.
III If a LPP admits an optimal solution, the objective function assumes the optimum value at an extreme point f the convex set generate3d by the et of all FS.
IV Solve the LPP by Simplex Method:
Maximize z=3x1 + 2x2
Subject to 2x1 + x2 ≤ 12
6x1 + 5x2 ≤ 40 and x1, x2 ≥ 0
V Find the minimum cost of transportation in the following problem:

VI Describe the ‘revised simplex algorithm, in solving Linear programming problem.
VII (a) Compare the relative advantages and disadvantages of the revised simplex method over the ordinary simplex method.
(b) Discuss the working principle of ‘Dual simplex method’ in solving a linear programming problem. Why is the method called as dual simplex method?
VIII (a) Customers arrive at a post office manned by a single person according to Poisson input process with mean rate of 10 per hour. The time required to serve a customer has an exponential distribution with a mean of 4 minutes. Find: (i) average number in the system (ii) the probability that there would be 2 customers in the queue.
(b) Draw spanning tree for the figure given below:

IX Write short notes on the following:

• PERT and CPM
• Minimum Cost Flow Problem
• Simulation

OPERATIONS RESEARCH - OR Paper 2 interview-questions

Download FREE Information Technology Engineering (IT Engg. Branch) Previous 5 Years solved Regular and Reappear Question Papers B.tech PTU 6th / 7th Semester (2007, 2006, 2005, 2004, 2003) and related Placement HR - Technical Interview Questions for subject OPERATIONS RESEARCH - OR

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.

OPERATIONS RESEARCH - OR Paper 3 interview-questions

Download FREE Information Technology Engineering (IT Engg. Branch) Previous 5 Years solved Regular and Reappear Question Papers B.tech PTU 8th Semester (2007, 2006, 2005, 2004, 2003) and related Placement HR - Technical Interview Questions for subject OPERATIONS RESEARCH - OR

OPERATIONS RESEARCH 6th Semester CS 322 (MAY 2005)
I
(a) What are decision variables?
(b) What are mixed inter-programming problems?
(c) What are the various types of games?
(d) What do you mean by modeling?
(e) Distinguish between PE and CPM
(f) What do you mean by the infeasible solution to a LP?
(g) What do you mean by the objective function?
(h) What is a balanced transportation problem?
(i) Why is Simulation used?
(j) What is a queue? Give an example.

II What is operations research? Describe briefly its applications?

III Determine the Initial Basic Feasible solution to the following transportation problem using row-minima rule:

From	To Available
	3	4	6	8	9	20
	2	10	1	5	8	30
	7	11	20	40	3	15
	2	1	9	14	16	13
Demand	40	6	8	18	6

IV Explain clearly the following terms:
(i) Strategy
(ii) Pay-off Matrix and
(iii) Saddle point

V A self service store employs one cashier at its counter. Nine customers arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service rate, find
(a) Average number of customers in the system
(b) Average number of customer in queue or average queue length
(c) Average tie a customer spends in the system.
(d) Average time a customer waits before being served.

VI Write a short note on Simulation using Monte- Carlo Method

VII Use duality to solve the LPP
Maximize z=2x1+x2
Subject to x1+2x2 = 10
x1+3x2 = 6
x1 - x2 = 2
x1 - 2x2 = 1
x1 , x2 = 0

VIII Discuss a suitable algorithm/ method to find the minimum spanning tree associated with a particular network/graph

IX Considering the following data for the activities concerning a project:

Name of the activity	A	B	C	D	E	F
Immediate predecessors	-	A	A	B,C	-	E
Estimated time (days)	2	3	4	6	2	8

(a) Draw a network diagram for the project
(b) Find the minimum project completion time
(c) List the bottleneck activities
(d) Find total float, free float and independent float for the various activities
(e) Find slack for various events