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ASSIGNMENT
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DRIVE FALL
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2013
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PROGRAM
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MBADS / MBAN2 / MBAHCSN3 / PGDBAN2 / MBAFLEX
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SEMESTER
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II
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SUBJECT CODE & NAME
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MB0048 OPERATIONS RESEARCH
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BK ID
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B1631
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CREDITS
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4
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MARKS
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60
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Note: Answer all questions. Kindly note that answers for 10 marks
questions should be approximately of 400 words. Each question is followed by
evaluation scheme.
1. Discuss the methodology of Operations Research. Explain in brief the
phases of Operations Research.
Answer : Meaning of Operations Research
Operations
research (OR) is an analytical method of problem-solving and
decision-making that is useful in the management of organizations. In
operations research, problems are broken down into basic components and then
solved in defined steps by mathematical analysis.
Methodology of Operations Research :
1. Operational Research
Techniques. Some methodological aspects of operational research, and some of
the main OR techniques, including: Critical Path Analysis, Production,
Scheduling, Markov Chains, Queueing Theory, Replacement, Simulation, Stock
Control, Dynamic Programming, Decision Theory, Theory of Games. OR202.
2. Mathematical Programming. Linear programming:
from the most basic introduction to sufficient conditions for optimality;
duality; sensitivity of the solution; discovery of the solution to small
problems by graphical methods, and proof of optimality by testing the
sufficient conditions; solution to larger problems by using a computer package.
The transportation programme: properties of solution, connection with graph theory,
an
2. a. Explain the graphical method of solving Linear Programming
Problem.
Answer :
1. Initially
we draw the coordinate system correlating to an axis the variable x, and the
other axis to variable y, as can see in the figure.
2. We
mark, in these axis, a numerical scale appropriate to the values it can take
the variables according to the constraints of the problem. To do this work, for
each constraint we must to void all variables except the related to a certain
axis, so we establishing the right value for such axis. This process must be
done for every axis.
3.
Following, we represent all constraints. We
take the first one and we draw the line that is obtained by considering the
constraint as an equality. In the figure, this is represented with the A-B
edge, and the region that
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.
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Machines
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Time per unit
(minutes)
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Machine capacity available (min.)
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Product A
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Product B
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Product C
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M1
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5
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3
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2
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400
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M2
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4
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-
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3
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500
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M3
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5
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2
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1
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300
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Answer :
3.Explain the steps involved in finding Initial Basic Feasible solution
by the following methods:
a. North West Corner Rule method
Answer : North West Corner Rule:
Step 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 there, that is X11 = min (a1, b1).
So that 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 the upper left hand corner (Small Square) of
cell (1, 1) in the transportation table.
Step 2: If b1 > a1 the capacity of origin O, is exhausted but
the requirement at destination D1 is still not satisfied, so that at least one
more other variable in the first column will have to take on a positive value.
Move down vertically to the second row and make the second allocation of
magnitude X21 = min (a2, b1 – x21) in the cell
b. Vogel’s approximation method
Answer : Vogel’s approximation
method:
Steps of the Vogel’s
Approximation Method to get the initial solution
1) Consider each row of the cost matrix individually and find the
difference between two least cost cells in it. Then repeat this for each
column. Identify the row or column with the largest difference (select any one
in case of a tie).
2) Now consider the cell with minimum cost in that column (or row) and
assign the maximal possible units to that cell.
3) Delete the row/column, if it is satisfied.
4) Again start with step 1 and calculate the differences, proceed in the
same manner as stated in earlier paragraph and continue until all units have
been assigned.
4. Explain Monte Carlo Simulation method. What are the advantages and
limitations of Simulation?
Answer : Monte Carlo simulation
is a computerized mathematical technique that allows people to account for
variability in their process to enhance quantitative analysis and decision
making. The technique is used by professionals in such widely disparate fields
as finance, project management, energy, manufacturing, engineering, research
and development, insurance, oil & gas, transportation, and the environment.
The expression "Monte Carlo
method" is actually very general. Monte Carlo (MC) methods are stochastic
techniques--meaning they are based on the use of random numbers and probability
statistics to investigate problems. You can find MC methods used in everything
from economics to nuclear physics to regulating the flow of traffic. Of course
the way they are applied varies widely from field to field, and there are
dozens of subsets of MC even within chemistry. But, strictly speaking, to call
something a "Monte Carlo" experiment, all you need to do is use random
numbers to examine some problem.
5. Explain the Characteristics and Constituents of a Queuing System.
Answer : Meaning of Queuing Theory:
In general, a queueing system
involves customers who enter the system, wait in line (a queue), are served,
and leave the system. While many familiar queueing situations involve only
people as customers and servers, there are also many applications in which one
or both of these entities is inanimate (e.g., an ATM could be the server’ parts
on an assembly line could be the ‘customers’). Nevertheless, the terms customer
and server are still used. The key features of queueing systems can be
classified as characteristics of arrivals, service discipline, and
characteristics of service.
Characteristics of a Queuing System
Two important issues relevant to
a queue involve the timing and types of arrivals. Usually, the timing of
arrivals is described by specifying the average rate of arrivals per unit of
time (a), or the average interarrival time (1/a).
There are at least two issues
related to the types of arrivals. First, the arrivals may occur one at a time
or in batches (such as a carload, for example). Second, the arrivals might well
be treated as essentially all the same, or they may
6.a. What do you mean by dominance? State the dominance rules for rows
and columns.
Answer : Dominance in ethology is
an "individual's preferential access to resources over another".[1]
Dominance in the context of biology and anthropology is the state of having
high social status relative to one or more other individuals, who react
submissively to dominant individuals. This enables the dominant individual to
obtain access to resources such as food or potential mates at the expense of
the submissive individual, without active aggression. The absence or reduction
of aggression means unnecessary energy expenditure and the risk of injury are
reduced for both. The opposite of dominance is submissiveness.
Dominance may be a purely dyadic
relationship, i.e. individual A is dominant over individual B, but this has no
implications for whether either of these is dominant over a third individual C.
Alternatively, dominance may be
b. What are the differences between PERT and CPM?
Answer : CPM vs. PERT
Project management is an
important part of every business enterprise. Whenever a new product or service
is launched; when embarking on a marketing campaign; or when organizing any new
projects; project management is needed to make everything organized and
successful.
As all projects consume resources
such as materials, time, people, and money; starting one would entail an
effective project management team and the right techniques to accomplish them,
especially those projects that are very complex ones.
A complex project would normally
encounter several delays and may surpass the budget allocated for it making a
project very costly and which may lead to losses. While many techniques fail in
solving these problems, there are two
Dear
students get fully solved assignments
Send
your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call
us at : 08263069601