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DRIVE
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SUMMER 2015
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PROGRAM
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MBA/ MBADS/ MBAFLEX/ MBAHCSN3/ PGDBAN2
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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.
Q. 1. What are the features of operations
research? What are the limitations of operations research?
Answer:Operations research OR means to apply scientific and mathematical methods
for decision making and problem solving.
OR does not provide decisions else it
provides quantitative data to the managers. The managers use this data for
making decisions.
OR tries to find better solutions to
different problems. Hence, it is used to solve complex management problems.
Q. 2. a. Explain the graphical method of
solving Linear Programming Problem.
Answer:Linear programming (LP; also called 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
b. A furniture manufacturing company plans
to make two products: chairs and tables- from its available resources, which
consists of 400 board feet of mahogany timber and 450 man-hours of labour. It
knows that to make a chair requires 5 board feet and 10 man-hours and yields a
profit of Rs.45 while each table uses 20 board feet and 15 man-hours and has a
profit of Rs.80.
Formulate the LPP to maximise the profit.
Answer:
Linear programming models
consist of an objective function and the constraints on that function. A linear
programming model takes the following form:
Objective function:
Z
= a1X1 +
a2X2 + a3X3
+ . . . + anXn
Q. 3. a. List the steps of the Vogel’s
Approximation Method(VAM) to find the initial feasible solution.
Answer:The Vogel approximation method (Unit cost penalty method) is an iterative
procedure for computing a basic feasible solution of a transportation problem.
This method is preferred over the two methods discussed in the previous
sections, because the initial basic feasible solution obtained by this method
is either optimal or very close to the optimal solution.
Steps in Vogel Approximation Method (VAM)
The standard instructions are paraphrased
below:
b. The XYZ manufacturing company has a
current transportation schedule which is being questioned by the top management
as to whether or not it is optimal. The firm has 3 factories and 5 warehouses.
The unit transportation costs (in Rs.), factory capacities, and ware house
requirements are given below. Find the initial feasible solution using Vogel’s
Approximation Method (VAM).
Answer:The task is to use VAM to allocate contractors to tasks. It scales to
large problems, so ideally keep sorts out of the iterative cycle. It works as
follows:
·
Step 1:
Balance the given transportation problem if either (total supply>total
demand) or (total supply<total demand)
·
Step 2:
Determine the penalty cost for each row and column by subtracting the lowest
cell cost in the row or column from the next
Q. 4. a. What is Integer Programming
Problem (IPP) ?
Answer: An integer programming problem is a mathematical optimization or
feasibility program in which some or all of the variables are restricted to be
integers. In many settings the term refers to integer linear programming (ILP),
in which the objective function and the constraints (other than the integer
constraints) are linear. Integer
programming is NP-hard. A special case, 0-1 integer linear programming, in
which unknowns are binary, and
b. Explain Gomory’s all integer algorithm
of an IPP.
Answer:A Gomory's Cut is a linear constraint with the property that it is
strictly stronger than its Parent, but it does not exclude any feasible integer
solution of the LP problem under consideration. It is used, in conjunction with
the Simplex Method, to generate optimal solutions to linear integer programming
problems (LIP). Formally the LP and LIP problems under consideration are as
follows:
LP: opt
ctx subject to Ax = b, x >= 0
LIP: opt
ctx subject to Ax = b, x >= 0 and integer
Q. 5. a. Explain Monte Carlo Simulation.
Answer: Monte Carlo
simulation is a computerized mathematical technique that allows people to
account for risk in 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.
Monte Carlo simulation
b. A Company produces 150 cars. But the production rate varies with the
distribution.
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:
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Production Rate
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Probability
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Cumulative probability
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RN Range
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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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149
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0.15
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0.30
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15-29
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150
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0.20
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0.50
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30 – 49
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151
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0.30
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0.80
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50 – 79
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152
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0.15
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0.95
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80 – 94
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153
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0.05
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1.00
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95 – 99
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Simulation for 10 days using the
given random numbers
Q. 6. a. Explain the dominance principle in
game theory
Answer: In game theory, strategic dominance (commonly called simply dominance)
occurs when one strategy is better than another strategy for one player, no
matter how that player's opponents may play. Many simple games can be solved
using dominance. The opposite, intransitivity, occurs in games where one
strategy may be better or worse than another strategy for one player, depending
on how the player's opponents may play.
c. Differentiate between PERT and CPM
Answer:CPM and PERT (Program Evaluation and Review Technique) are most commonly
used methods for project management. There are some similarities and
differences between PERT and CPM. PERT can be applied to any field requiring
planned, controlled and integrated work efforts to accomplish defined
objectives.CPM/
Dear
students get fully solved assignments
Send
your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call
us at : 08263069601
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