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DRIVE- Spring 2014
PROGRAM-MBADS / MBAN2 / MBAHCSN3
/ PGDBAN2 / MBAFLEX
SEMESTER- II
SUBJECT CODE & NAME- MB0048
OPERATIONS RESEARCH
Q1.
Discuss the methodology of Operations Research. Explain in brief the phases of
Operations Research. (Meaning of Operations Research, Methodology of Operations
Research, Phases of Operations Research) 2,4,4
Answer:
Definitions of operations
research
Churchman, Aackoff, and Aruoff
defined operations research as “the application of scientific methods,
techniques and tools to the operation of a system with optimum solutions to the
problems” where 'optimum' refers to the best possible alternative.
The objective of OR is to provide
a scientific basis to the decision-makers for solving problems involving
Q2. a. Explain the
graphical method of solving Linear Programming Problem.
b.
A paper mill produces two grades of paper viz., X and Y. Because of raw
material restrictions, it cannot produce more than 400 tons of grade X paper
and 300 tons of grade Y paper in a week. There are 160 production hours in a
week. It requires 0.20 and 0.40 hours to produce a ton of grade X and Y papers.
The mill earns a profit of Rs. 200 and Rs. 500 per ton of grade X and Y paper
respectively. Formulate this as a Linear Programming Problem.
Answer:
a.
Graphical Methods to Solve LPP
While obtaining the optimal
solution to an LPP by the graphical method, the
statement of the following
theorems of linear programming is used:
Q3. a. Explain how
to solve the degeneracy in transportation problems.
b. Explain the
procedure of MODI method of finding solution through optimality test.
(a. Degeneracy in
transportation problem, b. Procedure of MODI method ) 5, 5
Answer:
a.
Degeneracy in transportation problem
A basic solution to an m-origin,
n destination transportation problem can have at the most m+n-1 positive basic
variables (non-zero), otherwise the basic solution degenerates. It follows that
whenever the number of basic cells is less than m + n – 1, the transportation
problem is a degenerate one. The degeneracy can develop in two ways:
Q4.
a.
Explain the steps involved in Hungarian method of solving Assignment problems.
b.
Find an optimal solution to an assignment problem with the following cost
matrix:
Answer.
a.)
Hungarian
Method Algorithm
Hungarian method algorithm is
based on the concept of opportunity cost and is more efficient in solving
assignment problems. The following steps are adopted to solve an AP using the
Hungarian method algorithm.
Step 1: Prepare row ruled matrix
by selecting the minimum values for each row and subtract it from the other
elements of the row.
Step 2: Prepare column-reduced
matrix by subtracting minimum value of the column from the other
Q5. A) Explain Monte Carlo Simulations.
Answer: Monte
Carlo simulations, a statistical technique used to model probabilistic (or
“stochastic”) systems and establish the odds for a variety of outcomes. The
concept was first popularized right after World War II, to study nuclear
fission; mathematician Stanislaw Ulam coined the term in reference to an uncle
who loved playing the odds at the Monte Carlo casino (then a world symbol of
gambling, like Las Vegas today). Today there are multiple types of Monte Carlo
simulations, used in fields from particle physics to engineering, finance and
more.
B) A
Company produces 150 cars. But the production rate varies with the
distribution.
|
Production rate
|
147
|
148
|
149
|
150
|
151
|
152
|
153
|
|
Probability
|
0.05
|
0.10
|
0.15
|
0.20
|
0.30
|
0.15
|
0.05
|
At
present the track will hold 150 cars. Using the following random numbers
determine the average number of cars waiting for shipment in the company and
average number of empty space in the truck. Random Numbers 82, 54, 50, 96, 85,
34, 30, 02, 64, 47.
Answer.
Q6.
a. Explain the dominance principle in game theory.
b. Describe the Constituents of a Queuing System.
c. Differentiate between PERT and
CPM
a.
Dominance
In a rectangular game, the
pay-off matrix of player A is pay-off in one specific row ( r row ) th exceeding the
corresponding pay-off in another specific row( s row ) th . This means that whatever course of
action is adopted by player B, for A, the course of action Ar yields greater gains than the
course of action As .
Therefore, Ar is a better
strategy than As irrespective
of B’s strategy. Hence, you can say that Ar
dominates As .
Alternatively, if each pay-off in a specific column ( p column ) th is less than the corresponding
pay-off in another specific column( q
column ) th , it means strategy Bp offers minor loss
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