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Fall-2013
Master of
Business Administration - MBA Semester 2
MB0048-Operations Research-4 Credits
(Book ID:
B1631)
Assignment
(60 Marks)
Note: Answers
for 10 marks questions should be approximately of 400 words. Each question is
followed by evaluation scheme. Each Question carries 10 marks 6 X 10=60.
Q1. Discuss the
methodology of Operations Research. Explain in brief the phases of Operations
Research.
Answer. 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
scientists from
Q2. a. Explain the graphical method of solving Linear
Programming Problem.
b. A firm produces three types of products viz., A, B and C,
which are processed on three different machines viz., M1, M2 and M3. The time
required to process on unit of each of the products and the daily capacities of
machines available per day are given in the following table. The profit earned
by selling one unit of type A, B and C is Rs.10, Rs.15 and Rs.20 respectively.
It is assumed that what all is produced is consumed in the market. Formulate
this as Linear Programming Problem to maximize the profit.
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
Q3. Explain the steps involved in
finding Initial Basic Feasible solution by the following methods:
a. North West Corner Rule method
b. Vogel’s approximation method.
Answer. (a) North West Corner Rule method:
Steps 1 - The first
assignment is made in the cell occupying the upper left hand (north-west)
corner of the transportation table. The maximum feasible amount is allocated
here is: x11 = min (a1, b1)
Either the
capacity of origin O1 is used up or the requirement at destination D1 is
satisfied or both. This value of x11 is entered in
Q4. Explain Monte Carlo
Simulation method. What are the advantages and limitations of Simulation?
Answer. Monte Carlo Simulation method:
The Monte-Carlo
method is a simulation technique in which statistical distribution functions
are created by using a series of random numbers. This approach has the ability
to develop many months or years of data in a matter of few minutes on a digital
computer. The method is generally used to solve the problems that cannot be
adequately represented by mathematical models or where solution of the model is
not possible by analytical method. Let us now describe each step in detail.
Step 1: Define the
problem:
a) Identify the
objectives
Q5. Explain the Characteristics
and Constituents of a Queuing System.
Answer. Meaning of Queuing Theory:
A congestion system is system in which
there is a demand for resources for a system, and when the resources become
unavailable, those requesting the resources wait for them to become
available. The level of congestion in
such systems is usually measured by the waiting line, or queue, of resource requests (waiting line or queuing
models).
Operating
Characteristics of a Queuing System
A queuing model
has the following operating characteristics which enables us to understand and
efficiently manage a queue:
·
Queue length: The number of customers in the waiting
line reflects one of the two conditions. Short queues could mean
Q6. a. What do you mean by dominance?
State the dominance rules for rows and columns.
b. What are the differences
between PERT and CPM?
Answer. (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 .
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