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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)
Problem of Transportation Routes (20 Marks)
The
N&C Bank in Thailand is one of the biggest banks. There are 377 branches in
Bangkok and 3 distribution centers. Presently, it has experienced drivers who
take to the transportation routes. 27 vehicles are used on the 29 routes whose
capacity is the same. Two of the vehicles do overtime with taking two trips
each day. Some of the problems faced by N&S and formulated are: Each trip
will begin from its respective depot and end there. The route will remain the
same both morning and evening. The travelling time taken between each branch is
a known location and correct. The company is aware of 'the demand for capital
of each branch. Time of processing for every stop is same. for each branch.
Some of the limitations of this problem are: The volume of each vehicle is
firmly implemented by the insurance value per trip. Each branch's hours of
functioning depends upon its location. If the location is in the department
store, then the working hours will be from 11 am to 8 pin. If the location is
anywhere else, the working hours would be from 8.30 am to 3.30 pm. The
processing capacity of every depot or the distribution center (DC) is diverse
at the ratio of 50:30:20.
Each
distribution center works from 8.00 am to 5.00 pm. N&C aims at increasing
the transportation services along with the current resources. N&C has three
distribution centers which look after the picking up and delivery of cash to
and from every branch each day at different timings. The most appropriate
method for this problem would be the multiple depot routing problems with time limit.Nevertheless,
the new routes can bring changes in everyday process, i.e., change in
requirements, processing time, etc, hence, N&C requires a method to give
results in a short time operations. Two main methods are used. First,
development problem •is utilized. and capacitate VRPTW (vehicle routing problem
with time) is utilized later. The assignment problem gathers 377 branches into
3 groups, with each belonging to each distribution center and VRP'IW makes
daily routes for each distribution center. Consignment Problem method is used
for giving the tasks to the agents mating their positions, which can give a
very competent result. Vehicle rouong problem is the CVRP (capacitate vehicle
routing problem), a pr' Herb where all its customers need to be satisfied,
awareness of dumbfounds, and identifying all vetides, constrained capacity and
based at a central depot. The aim is to reduce the fleet of \•vehicles and
total commuting time at the same time as, total requirement of goods for each
route should not go beyond the capacity of the vehicle which plies on that
route. ":be most vital expansion of CVRP is the vehicle routing problem
with VRPTW (time window) which should serve each customer with a particular
time window.
Answer the following question.
Q1. Write
a short on the transportation system of N&C bank. (Hint: it has experienced
drivers who take to the transportation routes. 27 vehicles are used on the 29
routes whose capacity is the same,N&C has three distribution centers which
look after the picking up and delivery of cash to and from every branch each
day at different timings)
Q2.
What does CVRP stand for? (Hint: capacitated vehicle routing problem)
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 onl/' 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 interviewing 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)
CASE STUDY (20 Marks)
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.
Answer the following question.
Q1.
What is the Time Value of Money concept?
Q2.
What do you mean by present value of money?
Q3.
What is the Future Value of money?
Q4.
What the amount to be credited at the end of 5th year.
Assignment Solutions, Case study Answer sheets
Project Report and Thesis - Contact
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