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DRIVE- Fall 2014
PROGRAM-MBADS / MBAN2 / MBAHCSN3
/ PGDBAN2 / MBAFLEX
SEMESTER- II
SUBJECT CODE & NAME- MB0048
OPERATIONS RESEARCH
Q1
Explain the types of Operations Research Models. Briefly explain the phases of
Operations Research. (Meaning of Operations Research, Types of Operations
Research Models, 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
interaction with various components of the organisation. This can be achieved
by employing a team of
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:
·
The collection of all feasible solutions to an LPP
constitutes a convex set whose extreme points correspond to the basic feasible
solutions.
·
There are a finite number of basic feasible regions
within the feasible solution space.
·
If the convex set of the feasible solutions of the
system of simultaneous equation is a convex polyhedron, then at least one of the
extreme points gives an optimal solution.
·
If the optimal solution occurs at more than one
extreme point, the value of the objective function will be the same for all
convex combination of these extreme points.
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:
Case 1 - The degeneracy develops
while determining an initial assignment via any one of the initial
Q4.
a. Explain the steps
involved in Hungarian method of solving Assignment problems.
b.
What do you mean by unbalanced assignment problem? How do you overcome it?
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 values of that
column.
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.
Production rate and
probability
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
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