Quantitative Methods
Case
Studies
Linear
Programming (20 Marks)
Lexicographic Goal Programming is
used to solve a series of Linear Programming Model. This programming is used
wen . a goal has to be attained on•priority basis. Revenue budgeting is being
used to decide budget instead of a specific system in budget. Nevertheless,
revenue budget lays emphasis on the rising limitation of revenue while
estimating budget. The decision makers are limited due to the rising power of
capital and also the awareness of imminent restraints and fear of capital
resources. The goal is to raise the salary and allowance of the workers,to cut
down the operating cost, to raise the revenue expenses, to raise the capital
generated internally, and the cut down the overall budget. Some of the problems
are: insufficient allocation of funds and income, and• absence of importance of
order. The insufficient allotment occurred as the quantitative allotment models
were not used with power. . It is seen that the allotment of capital were not
being used in the right" way as a result the capital allotted to the labs
is drawn •in the maintenance of hostel. Various other changes also happen. In
fact, the funds allotted to the tertiary organizations are more often not
managed properly. The University of Owerri suffered and the progress of the
institution came down. There is absence of active teams for monitoring budget,
and so the budget can function in any manner. If the active teams to monitor
budget were present, the problem of mismanagement and the wrong use of it would
come down. Sundaram (1978) and Lee (1972) agreed that the various features of
target programming are, that it allows ordinal solution. According to Igniio
(1978), this tactic called Goal Programming, frequently symbolizes considerable
progress in the modeling and evaluation of the multi objective problems. This
shows that this area lets the systematic evaluation of a number of multi
objective problems which could include linear or non linear operations in the
incessant or separate variables. This is most successful in the research area.
The goal programming developed due to Charnes and Cooper, who suggested that
the model and method for dealing with some linear programming problems where
the contradictory 'goals of management' involed as limitations. Goal
programming method has been used for a number of programs. Goal programming
technique has solved the following problems: planning production in a ship
repairing company, smoothing production in 'just in time' production
atmosphere. The problem occurs when the model does not show the real
inclination of the decision maker. Noninferior solution in some cases many not
be essentially better than the lesser solution mainly in the case of natural resource
problem.
Answer
the following question.
Q1. What are the problems while
estimating the budget? (Hint: insufficient allocation of funds and income, and
absence of importance of order, The insufficient allotment occurred as the
quantitative allotment models were not used with power)
CASE
STUDY (20 Marks)
The cost of fuel in running of an
engine is proportional to the square of the speed and is Rs 48 per hour for
speed of 16 kilometers per hour. Other expenses amount to Rs 300 per hour. What
is the most economical speed?
Answer
the following question.
Q1. What is most economical speed?
Q2. What is a chisquare test?
Q3. What is sampling and what are
its uses.
Q4. Is there any alternative
formula to find the value of Chisquare?
Finoplastika
Industries Ltd, Nigeria (20 Marks)
Time series analysis has two
important aims: 1) recognizing the quality of the phenomenon shown by the
series of studies, and 2) Both the aims need the plan of the viewed time series
data is recognized and somewhat officially explained: A time series is said to
be a 'collection of observations made in sequence with time'. For example:
recording level of daily rainfall, periodical total domestic product of US, and
monthly strength of the. workers in Marine Corps for a specific rank and MOS.
The evaluation of time series gives instruments for picking a symbolic model
and delivering forecasts. There are two sorts of times series data: •
Continuous: in this the data consists of study at every moment, for example,
seismic movement recorded on a seismogram. • Discrete: the data contains
recordings taken at different periods ,like, statistics of each month crime.
Until the data is absolutely haphazard, studies in time series are usually
related to each and the following studies could be partly ascertain by the last
values. For instance, the reasons pertaining to the meteorology which have an
effect on the temperature for any given day tend to have some affect on the next
day's climate. Hence, the observations of the past temperature are helpful for
predicting temperatures for the following days. • A time series can be
deterministic if there are no haphazard or feasible features but goes in a set
and foreseeable manner. The data gathered during the classical physics
experiment like showing Newton's Law of Motion, is one example of a
deterministic time series. The stochastic type of series is more appropriate to
the econometric function. Stochastic variables contain undefined or arbitrary
viewpoint. Though the worth of each study cannot be precisely foreseen,
calculating the various observations could follow the expected method. These
methods can be explained through the statistical models. According to these
models, studies differ erratically on the underlying mean value whtch is the
role of time. Time series data can be put in the following categories: one or
more performance factors; trend, seasonality, cyclical function and random
sound. Various kinds of time series predicting models give forecasts through
extrapolating the previous performance of the values of a specified \'l!riable
of interest. Consecutive study in econometric times series are generally not
free and forecast can be made on the basis of last observations. Although
precise predictions can be made with deterministic time series, predictions of
stochastic time series are restricted to 'conditional statements regarding the
future on the basis of particular hypothesis.' Armstrong (2001) says, "The
basic Assumption is that the variable ui!! continue in the future as it has
behaved in the past. " Particularly, the time series predictions are
suitable for stochastic type of data in
which the fundamental root cause
of variation like, trend, cyclical performance, seasonality, and uneven
variations, do not change radically m time. Therefore, modeling is considered
to be more suitable temporarily instead of permanent predictions.
Answer
the following question.
Q1.
Write briefly on timeseries analysis. (Hint: recognizing the quality of the
phenomenon shown by the series of studies, and, both the aims need the plan of
the viewed time series data is recognized and somewhat officially explained)
CASE
STUDY (20 Marks)
The bulbs manufactured by a
company gave a mean life of 3000 hours with standard deviation of 400 hours. If
a bulb is selected at random, what is the probability it will have a mean life
less than 2000 hours?
Answer
the following question.
Q1. Calculate the probability.
Q2. In what situation does one
need probability theory?
Q3. Define the concept of sample
space, sample points and events in context of probability theory.
Q4. What is the difference between objective and
subjective probability?
Quantitative Methods
Case
Studies
Multi
Criteria Decision Making (20 Marks)
MCDA. (multi criteria decision
analysis) is considered to be one of the fastest growing research operations in
the last several years. The researcher focus towards MCDA led to development of
many different approaches and ways in the field. There are two types of
procedures: theoretical assumptions and decision addressed type. This
difference throws challenges to the prcedure of choosing the most ideal method
for the decision making problem. Most of the time, the initial approach towards
applying MCDA in the real world problems relates to the set up of simple
understanding Of the context and recognizing the problem of decision. This step
includes the ones• who make decisions and other important participants who make
important contributions for the MCDA procedure by sharing their knowledge. The
common insight of the decision framework is received by knowing the goals of
the decision making body and recognizing not only those people who make
decisions but also those who face the decision. • Dooley (2009) says that the
first three steps take up more time in the process of MCDA, particularly
because of their qualitative features. Assigning of comparative significant
weights to the selected criteria is the next step: These weights can be ascertained
directly, for example ranking, swing, trade off; or indirectly, for example
centrality, regression and interactive. Later, the DM has to give individual
scores, considering his or her views, to each of the recognized options
according to the criteria which seem vital. These scores show the decision of
DM . related to spreading of each substitute to every performance standard. The
information which is attained is maintained distinctively into performance
template, which is also as consequence matrix, options matrix, or just decision
table. The next process includes abstract of the information consisting of the
performance matrix in the form of multi criteria scores, for every possible
plan. Mostly, this is attained by combining the individual scores of matrix so
that total valuation of .each substitute which allows more comparison. The
groups of substitute ranked on the basis of all these scores. Finally, the
procedure can include a warm evaluation of the outcome to amendments in the
scores or criteria, to conclude the sturdiness of the result of MCDA. At the
end, the analysis and trade offs included in the respective choices are given
to and conferred with the DM. In many cases, the ultimate decision that DM
takes, does not match with the highest level of alternative, as they are more
focused towards the process of knowing the effect of each and every factor in
ranking of choices than in the exactness of the ranking. Also, it should be
observed that the generalizations are not used to of the outcome given by the
process of MCDA, and they only appropriate for the group of choices which were
assessed.
Answer
the following question.
Q1.
What role does MCDA play in decision making? (Hint: MCDA is considered to be
one of the fastest growing research operations, these scores show the decision
of DM related to spreading of each substitute to every performance standard)
Q2.
What does MCDA stand for? (Hint: multi criteria decision analysis)
Linear
Programming (20 Marks)
Lexicographic Goal Programming is
used to solve a series of Linear Programming Model. This programming is used
wen . a goal has to be attained on•priority basis. Revenue budgeting is being
used to decide budget instead of a specific system in budget. Nevertheless,
revenue budget lays emphasis on the rising limitation of revenue while
estimating budget. The decision makers are limited due to the rising power of
capital and also the awareness of imminent restraints and fear of capital
resources. The goal is to raise the salary and allowance of the workers,to cut
down the operating cost, to raise the revenue expenses, to raise the capital
generated internally, and the cut down the overall budget. Some of the problems
are: insufficient allocation of funds and income, and• absence of importance of
order. The insufficient allotment occurred as the quantitative allotment models
were not used with power. . It is seen that the allotment of capital were not
being used in the right" way as a result the capital allotted to the labs
is drawn •in the maintenance of hostel. Various other changes also happen. In
fact, the funds allotted to the tertiary organizations are more often not
managed properly. The University of Owerri suffered and the progress of the
institution came down. There is absence of active teams for monitoring budget,
and so the budget can function in any manner. If the active teams to monitor
budget were present, the problem of mismanagement and the wrong use of it would
come down. Sundaram (1978) and Lee (1972) agreed that the various features of
target programming are, that it allows ordinal solution. According to Igniio
(1978), this tactic called Goal Programming, frequently symbolizes considerable
progress in the modeling and evaluation of the multi objective problems. This
shows that this area lets the systematic evaluation of a number of multi
objective problems which could include linear or non linear operations in the
incessant or separate variables. This is most successful in the research area.
The goal programming developed due to Charnes and Cooper, who suggested that
the model and method for dealing with some linear programming problems where
the contradictory 'goals of management' involed as limitations. Goal
programming method has been used for a number of programs. Goal programming
technique has solved the following problems: planning production in a ship
repairing company, smoothing production in 'just in time' production
atmosphere. The problem occurs when the model does not show the real
inclination of the decision maker. Non inferior solution in some cases many not
be essentially better than the lesser solution mainly in the case of
natural resource problem.
Answer
the following question.
Q1.
What are the problems while estimating the budget? (Hint: insufficient
allocation of funds and income, and absence of importance of order, The
insufficient allotment occurred as the quantitative allotment models were not
used with power)
CASE
STUDY (20 Marks)
The cost of fuel in running of an
engine is proportional to the square of the speed and is Rs 48 per hour for
speed of 16 kilo meters per hour. Other expenses amount to Rs 300 per hour.
What is the most economical speed?
Answer
the following question.
Q1.
What is most economical speed?
Q2.
What is a chisquare test?
Q3.
What is sampling and what are its uses.
Q4.
Is there any alternative formula to find the value of Chisquare?
Finoplastika
Industries Ltd, Nigeria (20 Marks)
Time series analysis has two
important aims: 1) recognizing the quality of the phenomenon shown by the
series of studies, and 2) Both the aims need the plan of the viewed time series
data is recognized and somewhat officially explained: A time series is said to
be a 'collection of observations made in sequence with time'. For example:
recording level of daily rainfall, periodical total domestic product of US, and
monthly strength of the. workers in Marine Corps for a specific rank and MOS.
The evaluation of time series gives instruments for picking a symbolic model
and delivering forecasts. There are two sorts of times series data: •
Continuous: in this the data consists of study at every moment, for example,
seismic movement recorded on a seismogram. • Discrete: the data contains
recordings taken at different periods ,like, statistics of each month crime.
Until the data is absolutely haphazard, studies in time series are usually
related to each and the following studies could be partly ascertain by the last
values. For instance, the reasons pertaining to the meteorology which have an
effect on the temperature for any given day tend to have some affect on the
next day's climate. Hence, the observations of the past temperature are helpful
for predicting temperatures for the following days. • A time series can be
deterministic if there are no haphazard or feasible features but goes in a set
and foreseeable manner. The data gathered during the classical physics
experiment like showing Newton's Law of Motion, is one example of a
deterministic time series. The stochastic type of series is more appropriate to
the econometric function. Stochastic variables contain undefined or arbitrary
viewpoint. Though the worth of each study cannot be precisely foreseen,
calculating the various observations could follow the expected method. These
methods can be explained through the statistical models. According to these
models, studies differ erratically on the underlying mean value whtch is the
role of time. Time series data can be put in the following categories: one or
more performance factors; trend, seasonality, cyclical function and random
sound. Various kinds of time series predicting models give forecasts through
extrapolating the previous performance of the values of a specified \'l!riable
of interest. Consecutive study in econometric times series are generally not
free and forecast can be made on the basis of last observations. Although
precise predictions can be made with deterministic time series, predictions of
stochastic time series are restricted to 'conditional statements regarding the
future on the basis of particular hypothesis.' Armstrong (2001) says, "The
basic Assumption is that the variable ui!! continue in the future as it has
behaved in the past. " Particularly, the time series predictions are
suitable for stochastic type of data in which the fundamental root cause of
variation like, trend, cyclical performance, seasonality, and uneven
variations, do not change radically m time. Therefore, modeling is considered
to be more suitable temporarily instead of permanent predictions.
Answer
the following question.
Q1.
Write briefly on timeseries analysis. (Hint: recognizing the quality of the
phenomenon shown by the series of studies, and, both the aims need the plan of
the viewed time series data is recognized and somewhat officially explained)
Quantitative Methods
Case
Studies
Multi
Criteria Decision Making (20 Marks)
MCDA. (multi criteria decision
analysis) is considered to be one of the fastest growing research operations in
the last several years. The researcher focus towards MCDA led to development of
many different approaches and ways in the field. There are two types of procedures:
theoretical assumptions and decision addressed type. This difference throws
challenges to the prcedure of choosing the most ideal method for the decision
making problem. Most of the time, the initial approach towards applying MCDA in
the real world problems relates to the set up of simple understanding Of the
context and recognizing the problem of decision. This step includes the ones•
who make decisions and other important participants who make important
contributions for the MCDA procedure by sharing their knowledge. The common
insight of the decision framework is received by knowing the goals of the
decision making body and recognizing not only those people who make decisions
but also those who face the decision. • Dooley (2009) says that the first three
steps take up more time in the process of MCDA, particularly because of their
qualitative features. Assigning of comparative significant weights to the
selected criteria is the next step: These weights can be ascertained directly,
for example ranking, swing, trade off; or indirectly, for example centrality, regression and
interactive. Later, the DM has to give individual scores, considering his or
her views, to each of the recognized options according to the criteria which
seem vital. These scores show the decision of DM . related to spreading of each
substitute to every performance standard. The information which is attained is
maintained distinctively into performance template, which is also as
consequence matrix, options matrix, or just decision table. The next process
includes abstract of the information consisting of the performance matrix in
the form of multi criteria scores, for every possible plan. Mostly,
this is attained by combining the
individual scores of matrix so that total valuation of .each substitute which
allows more comparison. The groups of substitute ranked on the basis of all
these scores. Finally, the procedure can include a warm evaluation of the
outcome to amendments in the scores or criteria, to conclude the sturdiness of
the result of MCDA. At the end, the analysis and trade offs included in the
respective choices are given to and conferred with the DM. In many cases, the
ultimate decision that DM takes, does not match with the highest level of
alternative, as they are more focused towards the process of knowing the effect
of each and every factor in ranking of choices than in the exactness of the
ranking. Also, it should be observed that the generalizations are not used to
of the outcome given by the process of MCDA, and they only appropriate for the
group of choices which were assessed.
Answer
the following question.
Q1.
What role does MCDA play in decision making? (Hint: MCDA is considered to be
one of the fastest growing research operations, these scores show the decision
of DM related to spreading of each substitute to every performance standard)
Q2.
What does MCDA stand for? (Hint: multi criteria decision analysis)
A
monte Carlo Case Study (20 Marks)
Laura,' a 57 year old unmarried
woman, earns around 68,000 dollars per year with expenditure of 37,500 dollars.
She hit away 14,000 dollars each year and collected 330,000 dollars in her RRSP
and TFSA, and also a rented apartment worth 250,000 dollars. She has a iixed
pension given by her employer, although it is not indicated to price rise, and
Is entitled to get complete benefits of Canada Pension Plan and Old Age
Security, for retirement. She did not have a very competent portfolio: one
fourth of cash is there, and most of it was in contracted sector ETFs, single
stocks and business bonds. Due to wrong entry of ETFs in the account,
unnecessary taxes were charged. Even before reconstructing Laura's
portfolio,"he had to make certain that it matched with.her financial aims.
Laura's main aim was to ascertain if she could retire before the age of 65,
maybe as early as 60, therefore she had to know if her investments could
produce enough flow of cash after she retires. Monte Carlo may show a top
possibility of success with the allotment of equity of 70% ot 80%. Through a
risky questionnaire and art open interview, Justin Ill 'ascertain that Laura
was thebest person for a portfolio of 60% fixed income and 40% equities. .
Through Monte Carlo software, Justin entered
the current portfolio . size of Laura, her rate of savings, projected
retirement expenditure, and other employer income and government pensions. If
Laura feels that working till the age of 63 was unpleasant, she could go for
the reproduction again and with different estimation. Increasing her
anticipated returns or bringing down the rate of inflation, is only a thought,
therefore, she will have to make some stronger decisions: she will have to
making some more savings, or bring down her rate of planned expenses after
retirement. Amazingly, by bringing up the allotment to fixed salary could
increase her opportunity to succeed: in spite of th returns being lower than
the equities, the volatility is also less, which lessens the risk of helpless
decline in the early years. At last, Laura decided to work
for 6 more years and plan her
retirement at the age of 63. After this, Justin decided to help her make a
fresh ETF portfolio to match that goal: it was finalized at 30% short term
business bonds, 30% GICs, and the rest of it was divided among Canadian, L'S
and global equities. Laura was able to make a notified decision through the
Monte Carlo simulation, but this wasn't the end of the procedure. In two or
three years time, she will have to visit the location again to see that she is
still on the right path of her retirement goal, as many issues like, loss of
job, a legacy, new connections, increase in the interest rates, all these could
bring a change in the main suppusitions 1 ; and she will have to redo her plans.
The possibilities are different before the age of 63. For each added year that
Laura works, her portfolio will addition instead of a decrease and this will
lead to a thrilling difference: the success rate will rise
up by 25% points if she continues
to work till the age of 61 instead of 60.
Answer
the following question.
Q1.
How much was Laura earning at the age of 57? (Hint: 68,000 dollars per year)
A
Network Rail (20 Marks)
The railways play an important
role in the economy and infrastructure of Britain. Not very many people
travelled back jn the 1920 as compared to present time, in spite of 50%
reduction in raif routes as compared to the 1960s. Rail is also used for
transporting goods around Britain. Rail proves to be• more eco friendly and safest
means of transportation as compa;ed to other vehicles so, not surprisingly, the
number of people commuting have gone 40% more since the past ten years. By
2034, this figure can go up. The work of network rail has to look after the
tracks, bridges and tunnels which comprises of the British rail network. The
railway infrastructure is made up of signals and level crossings. It has to
look after the 20,000 mile long track and 40,000 bridges and tunnels. Britain's
18 main rail stations, from Edinburg Waverley to London King's Cross, are
looked after by the Britain rail system. Ten years ago, when the network rail
took up these responsibilities, • it had to face some challenges. The rail
neork was facing some problems. Trains were running late, the costs were too
high and there was shortage of assets in both the people and machinery. Due to
these issues, people had less confidence in the rail network. Ever since then,
rail network has aimed at sustaining operations to reduce the expenses. There
has been 28% reduction in expenses mainly because of conomy of scale. New
tracks and machinery havebeen bought, and there has been 90% rise in the rail
punctuality. Huge projects have been given on time an towards th budget, as a
result the confidence of the people has improved. Rail network has moved from
'find and fix' to 'predict and prevent' policy. This has proved to be more cost
effective and competent and enabled in avoiding delay or obstruction for the
people in their travel. The rail network invested approx. 12 billion pounds
between 2009 and 2014, towards the rail network. Britain has the fastest
developing network in whole of Europe. By investing in people, the rail network
is investing in the future to. .B ritain has the largest working personnel of
35,000 workers. It has people working in various positions, like, engineers for
maintenance and signaling to project managers. Each area offers an opportunity
to work. They also consist oi HR (human resources), IT (information
technology), and finance and customer service. Network Rail needs to employ and
keep capable engineers in order to get the work done. Presently, its engineers
are doing some oi the most stimulating projects in Europe. The projects include
HS2, which is the new super spted rail link between the north and south
Britain, and the project of London Crossrail. Some oi the biggest and busiest
rail stations are being upgraded, like, London King's Cross and Birmingham New
Street. The main focus of the HR of Network Rail is to recruit various
personnel. This not only deepens the culture of business but it also makes sure
that it can reach every talent. It offers training for every applicant, whether
he is a school dropout or a graduate, whether male or female, a continued flow
of appropriate talent is ensured to keep its long term project going. The
company abo gives many opportunities to its workers to receive recognized
qualifications, such as an exclusive programme in post graduation, sponsoring
the Master's Degree in project management and trainee.
Answer
the following question.
Q1.
What were the initial problems that Network Rail of Britain face? (Hint: It has
to look after the 20,000 mile long track and 40,000 bridges and tunnels. Trains
were running late, the costs were too high and there was shortage of assets in
both the people and machinery)
Q2.
What is the new super speed rail link between the north and south Britain
called? (Hint: HS2)
CASE STUDY
The bulbs manufactured by a
company gave a mean life of 3000 hours with standard deviation of 400 hours. If
a bulb is selected at random, what is the probability it will have a mean life
less than 2000 hours?
Answer
the following question.
Q1. Calculate the probability.
Q2. In what situation does one
need probability theory?
Q3. Define the concept of sample
space, sample points and events in context of probability theory.
Q4. What is the difference between objective and
subjective probability?
SUBJECT
: QUANTITATIVE METHODS
CASE STUDY: 1
The bulbs
manufactured by a company gave a mean life of 3000 hours with standard
deviation of 400 hours. If a bulb is selected at random, what is the
probability it will have a mean life less than 2000 hours?
Question:
1) Calculate the probability.
2) In what situation does one need probability theory?
3)
Define
the concept of sample space, sample points and events in context of probability
theory.
4) What is the difference between objective and subjective
probability?
CASE
STUDY : 2
The price P per unit at which a
company can sell all that it produces is given by the function P(x) = 300 — 4x.
The cost function is c(x) = 500 + 28x where x is the number of units produced.
Find x so that the profit is maximum.
Question:
1) Find the value of x.
2)
In
using regression analysis for making predictions what are the assumptions
involved.
3) What is a simple linear regression model?
CASE STUDY : 3
Mr Sehwag invests Rs 2000 every year
with a company, which pays interest at 10% p.a. He allows his deposit to
accumulate at C.I. Find the amount to the credit of the person at the end of 5th
year.
Question :
1) What is the Time Value of Money concept.
2) What do you mean by present value of money?
3) What is the Future Value of money.
4) What the amount to be credited at the end of 5th
year.
CASE
STUDY : 4
The cost of fuel in running of an
engine is proportional to the square of the speed and is Rs 48 per hour for speed
of 16 kilometers per hour. Other expenses amount to Rs 300 per hour. What is
the most economical speed?
Question:
1) What is most economical speed?
2) What is a chi-square test?
3) What is sampling and what are its uses.
4) Is there any alternative formula to find the value of
Chi-square?
Quantitative
Methods
1. Three numbers, whose sum is
12, are in AP. If 1,2 and 6 are added to them, the resultin g
numbers are in GP. Find the
numbers
2. Average rainfall on a city
from Monday to Saturday is 0.3 inch. Due to heavy rainfall on
Sunday, the average rainfall for
the week increased to 0.5 inch. What was the rainfall on
Sunday?
4. Given the following results of
the height and weight of 1000 students. The mean height is 170 cm, the mean
weight is 75 kg. the standard deviation of the height and weight are 6 cm and 6
kg respectively r = 0.6. amit weighs 50 kg, sumeet is 1.5 m tall. Estimate the
height of Amit from his weight and the weight of sumeet from his height
5. In a sample of 500 people from
a village in rajasthan, 280 are found to be rice eaters and rest wheat eaters.
Can we assume that both the food articles are equally popular?
6. In a binomial distribution 31%
of the items are under 45 and 8% are over 64. Find the mean and variance of the
distribution
7. In a large number of group of
children 55% are under 60 cm heighty nd 40% are between 60 and 65 cm. Assuming
a normal distribution, find the mean and SD of height
SUBJECT : QUANTITATIVE METHODS
Total
Marks: 80
Note : All Questions are Compulsory
Each
Question Carries Equal Marks 10 Marks
5) What
is model and give 4 examples . State their properties , advantages and
limitation.
6) What are the
types of inventories ? explain
7)
What is replacement problem ? Describe
some important replacement situation and policies ?
8) What
is operation Research ? Account for the growing importance Research in business
?
9) Briefly discuss
the Delphi method of making forecasts.
10)
Define an OR model and give 4 examples.
State properties, advantages & limitations
11)
How do you distinguish between resource
leveling and resource allocation problems? State and explain an algorithm for
resource allocation.
12)
What are different types of inventories?
Explain. What functions does inventory perform? State the two basic inventory
decisions management must make as they attempt to accomplish the functions of
inventory just described by you.
Quantitative Methods
Case Studies
Finoplastika Industries Ltd,
Nigeria (20 Marks)
Time series analysis has two
important aims: 1) recognizing the quality of the phenomenon shown by the
series of studies, and 2) Both the aims need the plan of the viewed time series
data is recognized and somewhat officially explained: A time series is said to
be a 'collection of observations made in sequence with time'. For example:
recording level of daily rainfall, periodical total domestic product of US, and
monthly strength of the. workers in Marine Corps for a specific rank and MOS.
The evaluation of time series gives instruments for picking a symbolic model
and delivering forecasts. There are two sorts of times series data: •
Continuous: in this the data consists of study at every moment, for example,
seismic movement recorded on a seismogram. • Discrete: the data contains
recordings taken at different periods ,like, statistics of each month crime.
Until the data is absolutely haphazard, studies in time series are usually
related to each and the following studies could be partly ascertain by the last
values. For instance, the reasons pertaining to the meteorology which have an
effect on the temperature for any given day tend to have some affect on the
next day's climate. Hence, the observations of the past temperature are helpful
for predicting temperatures for the following days. • A time series can be
deterministic if there are no haphazard or feasible features but goes in a set
and foreseeable manner. The data gathered during the classical physics
experiment like showing Newton's Law of Motion, is one example of a
deterministic time series. The stochastic type of series is more appropriate to
the econometric function. Stochastic variables contain undefined or arbitrary
viewpoint. Though the worth of each study cannot be precisely foreseen,
calculating the various observations could follow the expected method. These
methods can be explained through the statistical models. According to these
models, studies differ erratically on the underlying mean value whtch is the
role of time. Time series data can be put in the following categories: one or
more performance factors; trend, seasonality, cyclical function and random
sound. Various kinds of time series predicting models give forecasts through
extrapolating the previous performance of the values of a specified \'l!riable
of interest. Consecutive study in econometric times series are generally not
free and forecast can be made on the basis of last observations. Although
precise predictions can be made with deterministic time series, predictions of
stochastic time series are restricted to 'conditional statements regarding the
future on the basis of particular hypothesis.' Armstrong (2001) says, "The
basic Assumption is that the variable ui!! continue in the future as it has
behaved in the past. " Particularly, the time series predictions are
suitable for stochastic type of data in which the fundamental root cause of
variation like, trend, cyclical performance, seasonality, and uneven
variations, do not change radically m time. Therefore, modeling is considered to
be more suitable temporarily instead of permanent predictions.
Answer
the following question.
Q1. Write briefly on time series
analysis. (Hint: recognizing the quality of the phenomenon shown by the series
of studies, and, both the aims need the plan of the viewed time series data is
recognized and somewhat officially explained)
A Network Rail (20 Marks)
The railways play an important
role in the economy and infrastructure of Britain. Not very many people
travelled back in the 1920 as compared to present time, in spite of 50%
reduction in rail routes as compared to the 1960s. Rail is also used for
transporting goods around Britain. Rail proves to be• more eco-friendly and
safest means of transportation as compared to other vehicles so, not surprisingly,
the number of people commuting have gone 40% more since the past ten years. By
2034, this figure can go up. The work of network rail has to look after the
tracks, bridges and tunnels which comprises of the British rail network. The
railway infrastructure is made up of signals and level crossings. It has to
look after the 20,000 mile long track and 40,000 bridges and tunnels. Britain's
18 main rail stations, from Edinburg Waverley to London King's Cross, are
looked after by the Britain rail system. Ten years ago, when the network rail
took up these responsibilities, • it had to face some challenges. The rail
network was facing some
problems. Trains were running
late, the costs were too high and there was shortage of assets in both the
people and machinery. Due to these issues, people had less confidence in the
rail network. Ever since then, rail network has aimed at sustaining operations
to reduce the expenses. There has been 28% reduction in expenses mainly because
of economy of scale. New tracks and machinery have been bought, and there has
been 90% rise in the rail punctuality. Huge projects have been given on time an
towards th budget, as a result the confidence of the people has improved. Rail
network has moved from 'find and fix' to 'predict and prevent' policy. This has
proved to be more cost effective and competent and enabled in avoiding delay or
obstruction for the people in their travel. The rail network invested approx.
12 billion pounds between 2009 and 2014, towards the rail network. Britain has
the fastest developing network in whole of Europe. By investing in people, the
rail network is investing in the future to. .Britain has the largest working
personnel of 35,000 workers. It has people working in various positions, like,
engineers for maintenance and signaling to project managers. Each area offers
an opportunity to work. They also consist of HR (human resources), IT
(information technology), and finance and customer service. Network Rail needs
to employ and keep capable engineers in order to get the work done. Presently,
its engineers are doing some of the most stimulating projects in Europe. The
projects include HS2, which is the new super spotted rail link between the
north and south Britain, and the project of London Cross rail. Some of the
biggest and busiest rail stations are being upgraded, like, London King's Cross
and Birmingham New Street. The main focus of the HR of Network Rail is to
recruit various
personnel. This not only deepens
the culture of business but it also makes sure that it can reach every talent.
It offers training for every applicant, whether he is a school drop-out or a
graduate, whether male or female, a continued flow of appropriate talent is
ensured to keep its long term project going. The company gives many opportunities
to its workers to receive recognized qualifications, such as an exclusive
programme in post graduation, sponsoring the Master's Degree in project
management and trainee.
Answer the following question.
Answer
the following question.
Q1.
What were the initial problems that Network Rail of Britain face? (Hint: It has
to look after the 20,000 mile long track and 40,000 bridges and tunnels. Trains
were running late, the costs were too high and there was shortage of assets in
both the people and machinery).
Q2. What is the new super speed
rail link between the north and south Britain called? (Hint: HS2)
Case (20 Marks)
Since 9/11•terrorism has cased
threat attacks which have drawn the attention of political and media world. The
US had to launch. A 'war on terror' and applied a range of counteract terrorism
safety measures towards aviation, public transportation, ports, borders, public
gMhermg places, etc. While these steps may show cheap course of act!on by
government and security services, it is quite expensive. According to the
calculations done by Mueller and Stewart (2011), the expenditure of US homeland
and security has gone over 1.1 trillion dollars, which includes federal, state
and domestic government, and private sector, and also the cost of opportunity.
The Iraq an Afghanistan wars have added 1.2 trillion dollars to this
expenditure. The expenditure of federal, state and local US government on home
ground security has been estimated to 75 billion dollars more than the last
levels of 2001. It is seen that US is not the only country to be in these high
level of expenses, even though no other country can match its per capita or GDP
expenditure. For example, increased expenditure• on homeland security in UK,
Canada and Australia is nearly one half to one quarter of US expenditure per
capita or GDP. Nevertheless, in 2009, the government spent nearly 141.6 billion
dollars each year on homeland security. This figure is expected to reach about
300 billion dollars by 2016. After 9/11, the main objective has been to prevent
or alleviate any harm or casualty as a result of terrorism. The main issue is,
if this expenditure of counteracting terrorism been invested in a way that has
increased the cost of security of the public efficiently or not. Hence, the
commission report of 9/11, among other issues, was called upon • the US
government to execute safety measures which show evaluation of risks and
effectiveness of expenditure. Nevertheless, while the US needs to. evaluate
expenditure benefits for government regulations, such evaluation seems co have
not been done for homeland security in general, or for the DHS (department of homeland
security). One of
the causes could be that DHS is
not able to take up such evaluation. The NRC (national research council)
committee of the National Academics of Sciences, Engineering and Medicine, made
a request through S Congress to evaluate the functions of DHS, which was
working on the project for almost 2 years, came up with some surprising
result-. Besides evaluation of natural disasters, the committee 'did not find
any DHS risk analysis capabilities and methods that are yet adequate for supporting
DHS decision making.' Due to which, very less confidence could be had in most
of the risk evaluation done by DHS. The committee said that "it is not yet
clear that DHS is on a I ! trajectory for development of methods and capability
that is sufficient to ensure reliable risk analyses". Usually the
government and their rigid agencies shoo a neutral behaviour towards their
decision making. Stewart says that "the standard criterion for deciding
whether a government; programme can be justified on economic principles is net
present rnlue – the discounted monetized value of expected net benefits (i.e.,
benefits minus costs)" and that "e'Cpecttd values (an unbiased
estimate) is the appropriate estimate for use" (UMB, 1992).
Answer
the following question.
Q1.
The government spent nearly 141.6 billion dollars each year on 1 1 il (Hint:
homeland security)
Case (20 Marks)
Restaurants can avoid losing
customers because of long waiting queues. Some restaurants have chairs to help
customers sit and wait, which they put on the safe side, and remove the chairs
as time goes on. Nevertheless, putting waiting chair is 9ot the online solution
when the customers would go back and prefer-going to another place, there ls a
need to improve the service time-. The restaurant management needs to
understand the situation in a better way through numerical model. A data was
taken from a restaurant in Jakarta. Little's Theorem and M/Ml queuing model was
used to get the ration of arrival, service, utilization, waiting time and likelihood
of probable customers. At Sushi Tei, the customers' arrival rate during the
busiest time of the day is 2.22 customers/minute (cpm), while the service is
2.24 cpm. The average number of customers is 1.22 and that of utilization
period is 0.991. The study of queuing or waiting lines is called the Queuing
Theory. The evaluation taken after using the Queuing Theory includes - expected
waiting time in line, average time in the system, length of the line,
anticipated number of customers being served at one time, possibility of
customers that cringe, and the possibility of the system in some states, like
unoccupied or occupied. This data was taken after the inte,rviewing the
restaurant manager of Sushi Tei, and the data collected through the
observations at the restaurant. The rate of visiting customers was taken from
the restaurant. The restaurant used to keep a record of its everyday routine
work. The manager of the restaurant was interviewed to find about the capacity
of the restaurant, number of waiters and waitresses working there, and also the
number of cooks. It was observed that the M/M/1 operation was best suited for
the queuing model of the restaurant. This shows , that the time of arrival and
service are distributed proportionately. The system .of the restaurant
contained only one server. It was observed that, though there were a number of
waitresses in the restaurant, only one cook was there to serve
all the customers. According to
the analysis done on the functioning of the restaurant, on an average each
customer would spend 55 minutes, the length of the queue is approx. 36
customers, and the waiting time rs apprc;. 15 i ! minutes on average. It is
seen that the waiting time is not different from the theoretical waiting time.
it is assumed that the possible customers will begin to withdraw on seeing more
than 10 people ahead of them in the queue. It is also observed that, on
average, the customer can only tolerate 40 people in the queue. Since the
capacity of the restaurant is for 120 customers when fully occupied, the
possibility of 10 customers in a queue can be calculated as against 130 in the
system, i.e., 120 occupants in the restaurant and 10 or more waiting in the
queue. A simulation model will be developed for the restaurant. Through this
simulation, the analytical model results can be attained. Also, the simulation
model will help in adding more difficulty so the model can reflect the exact
operation of the restaurant more personally.
Answer
the following question.
Q1.
What are the reasons that show that DHS is incapable in evaluating the risks of
national security? (Hint: while the CS needs to evaluate expenditure benefits•
for government regulations, such evaluation seem to have not been done for
homeland security in general, DHS is not able to take up such evaluation.)
Q2.
The government spent nearly 141.6 billion dollars each year on (Hint: homeland
security)
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