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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 withvariouscomponents 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

2. statement of the following theorems of linear programming is used:
· The collection of all feasiblesolutions 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 solutionoccurs at morethan oneextremepoint, thevalueof 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:
Case1 - The degeneracy develops whiledetermining 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 assignmentproblems. Thefollowing steps areadopted 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.

3. Answer: MonteCarlo simulations, a statistical techniqueused to model probabilistic (or
“stochastic”) systems and establish theodds for a variety of outcomes. Theconcept was
first popularized right after World War II, to study nuclear fission; mathematician
Stanislaw Ulam coined theterm in reference to an uncle who loved playing theodds at
theMonteCarlo casino (then a world symbol of gambling, likeLas Vegas today). Today
there aremultipletypes of MonteCarlo simulations, used in fields from particlephysics
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 ingame theory.
b. Describe the Constituentsofa QueuingSystem.
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
Dear students get fully solved SMU MBA Fall 2014 assignments
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