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Quantitative Methods
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)
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?
Linear Programming for Parking Slot Optimization (20 Marks)
For the development of any country, transportations play a very vital and planned role, especially for distributing the goods of the progress of all the citizens. Traffic jam is the most common problem in transportation in urban are;s. One of the main causes of traffic jam is making the road diameter smaller for creating street parking on one side of the road. If seen expansively, traffic jam has a great affect. For example, one of the affects is due to extensive usage of fuel which leads to huge amount 'Of financial loss. Therefore, there is a great need for• reducing te traffic jam, and one of them is the problem of on street parking. The onstreet parking is the most serious problem and is the reason for problem of smooth traffic flow. Yosritzal and Widanengsih did a survey on the demand for parking based on the parking sites: They also recommended that the method of deterioration could be used to ascertain the level of parking area around the hospitals. • The parking according to the area, has been divided into r,vo groups: street parking and off street parking. PCU (parking control unit) is rhe space for parking vehicles, that depends on the dimension of that vehicle and the• added space required for maneuvering the vehicle, depending upon the angle of parking. •This survey was done at Jln.T.Panglima Polem Peunayong Banda Aceh, and was started in the morning at 7 and went on till 6 in the evening. . The technique of getting geometric data for parking space and the present parking space capacity is taken by measuring the area and space allocation of parking for each vehicle. The data collection for each vehicle which enters and leaves the parking lot along with the parking duration is taken after • making walking field survey along the parking lot and counting the vehicles and the time duration of parking. According th.e field survey data, model evaluation is done by involving the demand of user parking lot to average of accumulation of parking and of the duration of parking. The average of accumulation of parking is calculated after each 15 minutes for every vehicle. The solution to this problem is to increase the space capacity at Jalan PanglimaPolem in relation to the parking space availability, and meet the requirement of parking lor for each vehicle. The average of accumulation of parking in every 15 minutes for every vehicle is calculated from the average accumulation divided by the sum of average accumulation for all the vehicles and multiplied by the capacity of the parking space. The outcome of this study shows that the formulation of maximizing the allocation of parking lot gives considerable ,atious results when the formulation regards different \•iewpoints of the needs and demands of parking. Maximizing problem occurs on fulfilling all the demands and needs of parking without any possible area in the maximization ..The most significant feature comes within the formulation before taking consideration the other features to look for actual maximum outcome for the problem.
Answer the following question.
Q1. What remedy was taken for solving the problem of parking space at Jalan T. Panglima Polem? (Hint: to increase the space, the average of accumulation of parking in every 15 minutes for every vehicle is calculated from the average accumulation dhided by the sum of average accumulation for all the vehicles and multiplied by the capacity of the parking space.)
Q2. Traffic jam is the most common problem in transportation in urban areas. True/False (Hint: True)
Case (20 Marks)
Due to the changing requirements for the products, the inventory management has become a vital component, particularly for the safety of the stock. The four eements for evaluating the (J.f?.Ck safety ••• are: forecast requirement, level of service, start time and '!fie definite demand. The purpose of safety stock is to safeguard against this probability, but the problem is more than the high safety stock and the need can increase the operational costs. On the basis of these difficulties, the prediction needs to be exact so that the company can ascertain the amount needed to be bought, manufactured and shipped. For estimating the forecast, the dual exponential smoothing model is f applied. With. the use of exponential smoothing, calculation for both the average and the trend can be smoothed. • Not just prediction, lead time also is the main component for ,l ascertaining the safety stock and aspects which can bring down the stock out case. "Lead time is the time elapsed in between the receipt of customer order until the delivery of finished goods to the customer". Some of the issues of lead time are: demand, order of .quantity, product quality, reorder spot, safety stock, and other price issues such as discount, permit shortage or not, price rise and the value of time of money, and should be considered in deduction of lead time. On the basis of the stock out occurrences, there is an issue which affects the case. Forecasting and reorder point also affect the safety stock. When the safety stock reaches the right stage, the stock level is brought down. Nevertheless, forecasting influences the estimation of safety stock, as the level of safety stock is ascertained on the basis of forecasting estimations. Not only this, the reorder point can ascertain the level of safety stock.A stock out or pending orders is a state which the company experiences for not meeting the requirements of the customer within the required time period. Each month, PT.Combiphar acquired stock outs in very high levels and values. Research was done on CTS3 or Omtusi, since they have their quantity, rate and value is very high. Comtusi Syrup is a cough syrup which is produced by PT.Combiphar, Padalarang, Indonesia. It is prepared for hospital purposes and pharmacists, and comes in 60ml pack. The quantity of total stok out in 2012 was 1,390,698 units, and the total value was Rp 35,229,335. The total stock out quantity of CTS3 is at the rate of 9%; the quantity is equal to 128,036 units. The percentage of this product is 9.75% from the total value, which is Rp 3,424,963,000. Due to the above case of stock out, the capital and total profit came down. The above estimations show considerable difference in the profits because of stock out case. The company did not face any loss, but the profits came down. Because of stock out in 2012, the loss of Rp 1, 888,383,500 was seen by the company. According to the above evaluation, it is clear that the company had to face the dilapidated profits because of stock out condition.
Answer the following question.
Q1. Write a short note on Forecasting, ReOrder Point and Safety Stock Level at PT. Combiphar, Indonesia. (Hint: The four elements for evaluating the stock safety are: forecast requirement, level of service, start time and the definite demand, The purpose of safety stock is to safeguard against this probability, but the problem is more than the high safety stock and the need can increase the operational costs)
Q2. Which cough syrup does PT.Combiphar make? (Hint: comtusi)
Assignment Solutions, Case study Answer sheets
Project Report and Thesis - Contact
ARAVIND – 09901366442 – 09902787224
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