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ASSIGNMENT
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DRIVE
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WINTER
2014
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PROGRAM
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MBADS/
MBAFLEX/ MBAHCSN3/ MBAN2/ PGDBAN2
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SUBJECT
CODE & NAME
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MB0048- OPERATIONS RESEARCH
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SEMESTER
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2
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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.
Q.1. Explain the types of Operations
Research Models. Briefly explain the phases of Operations Research.
Answer:
Types of Operations Research Models
A
model is an idealized representation or abstraction of a real-life system. The
objective of a model is to identify significant factors that affect the
real-life system and their interrelationships. A model aids the decision-making
process as it provides a simplified description of complexities and uncertainties
of a problem in a logical structure. The most significant advantage of a model
is that it does not interfere with the real-life system.
Classification
of OR models
You can broadly classify OR models
into the following types.
a. Physical Models
include all form of diagrams,
2a. Explain the graphical method of solving Linear Programming
Problem.
Answer:
Linear programming (LP or linear optimization) is a method to achieve the best
outcome (such as maximum profit or lowest cost) in a mathematical model whose
requirements are represented by linear relationships. Linear programming is a
special case of mathematical programming (mathematical optimization).
More
formally, linear programming is a technique for the optimization of a linear
objective function, subject to linear equality and linear inequality
constraints. It’s feasible region is a convex polyhedron, which is a set
defined as the intersection of finitely many half spaces, each of which is
defined by a linear inequality.
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 awake. 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 :
Objective function is to maximize the profit
Thus Max. Z=200X1+500X2
Constraints 1.Raw
materials
2. Production hour.
LPP is
3 a. Explain how to solve the degeneracy in transportation
problems.
Answer: There is a type of linear programming
problem that may be solved using a simplified version of the simplex technique
called transportation method. Because of its major application in solving
problems involving several product sources and several destinations of
products, this type of problem is frequently called the transportation problem.
It gets its name from its application to
b. Explain the procedure of MODI method of finding solution
through optimality test.
Answer: Transportation Algorithm for Minimization
Problem (MODI Method)
After evaluating an initial basic feasible
solution to a transportation problem, the next question is how to get the optimum
solution. The basic techniques are illustrated as follows:
1. Determine the net evaluations for the
non–basic variables (empty cells)
2. Determine the entering variable
3. Determine the leaving variable
4. Compute a better basic feasible solution
4
a. Explain the steps involved in Hungarian method of solving Assignment
problems.
Answer: The
assignment problem is one of the fundamental combinatorial optimization
problems in the branch of optimization or operations research in mathematics.
It consists of finding a maximum weight matching in a weighted bipartite graph.
In
its most general form, the problem is as follows:
There
are a number of agents and a number of tasks. Any agent can be assigned to
perform any task, incurring some cost that may vary
b. What do you mean by unbalanced
assignment problem? How do you overcome it?
Answer:
Unbalanced
assignment problem: This is the case of assignment
problem where the number of persons is not equal to the number of jobs. A dummy
variable, either for a person or job (
as it required) is introduced with zero
cost or time to make it a balanced one.
If
number of jobs is not equal to the number of operators then the assignment
problem is known as unbalanced assignment problem. In other words in a pay off
matrix of assignment problem if number of rows and number of columns are not
equal then it is unbalanced assignment problem.
To solve
unbalanced assignment prob
Q5.a. Explain the Monte Carlo Simulation.
Answer: Monte Carlo methods (or Monte Carlo
experiments) are a broad class of computational algorithms that rely on
repeated random sampling to obtain numerical results; typically one runs
simulations many times over in order to obtain the distribution of an unknown
probabilistic entity. The name comes from the resemblance of the technique to
the act of playing and recording your results in a real gambling casino. They
are often used in physical and mathematical problems and are most useful when
it is difficult or impossible to obtain a closed-form expression, or
b. A Company produces 150 cars. But the production rate varies
with the distribution.
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Production Rate
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Probability
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147
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0.05
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148
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0.10
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149
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0.15
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150
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0.20
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151
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0.30
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152
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0.15
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153
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0.05
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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. 5 +5 =
10 marks(200 - 250 words each)
Answer:
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Production Rate
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Probability
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Cum. Probability
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Random Numbers
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147
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0.05
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0.05
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00-04
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148
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0.10
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0.15
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05-14
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6 a. Explain the dominance principle in game theory.
Answer: Game
theory is a study of strategic decision making. Specifically, it is "the
study of mathematical models of conflict and cooperation between intelligent
rational decision-makers".[1] An alternative term suggested "as a
more descriptive name for the discipline" is interactive decision theory.[2]
Game theory is mainly used in economics, political science, and psychology, as
well as logic and biology. The subject first addressed zero-sum games, such
that one person's gains exactly equal net losses of the other participant or
participants. Today, however, game theory applies to a wide range of behavioral
relations, and has developed into an umbrella term for the logical side of
decision science, including both humans and non-humans (e.g. computers).
b. Describe the Constituents of a Queuing System.
Answer:
Characteristics of a queuing system that impact its performance, for example,
queuing requirements of a restaurant will depend upon factors like:
·
How do customers arrive in the
restaurant? Are customer arrivals more during lunch and dinnertime (a regular
restaurant)? Or is the customer traffic more uniformly distributed (a cafe)?
·
How much time do customers spend in
the restaurant? Do customers typically leave the restaurant in a fixed amount
of time? Does the customer service time vary with the type of customer?
c. Differentiate between PERT and CPM
Answer: 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.
Dear students get fully solved SMU MBA Fall 2014 assignments
Send your semester &
Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
(Prefer mailing. Call in emergency )