OPERATIONS RESEARCH - OR Paper 3

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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