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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
ARAVIND – 09901366442 – 09902787224
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