Quantitative Tech & Methods

Posted on September 13, 2019September 13, 2019 by gani37

Quantitative Methods

A Network Rail

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. Du 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 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. .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 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 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?

Case Study 3

Problem of Transportation Routes

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 vet-ides, 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 Study

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 re-order 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, Re-Order 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)36.

Quantitative Methods

Case Studies

Finoplastika Industries Ltd, Nigeria

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

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?

Problem of Transportation Routes

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 RPTW (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 vet-ides, 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.

Q2. What does CVRP stand for? (Hint: capacitated vehicle routing problem)

Case Study

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, publicgMhermg 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 thse 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 invest.ed 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 e’•aluation 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”. l.sually the government and their rigid agencies shoo a neutral behavior 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)

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

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.

Q2. What is the new super speed rail link between the north and south Britain called? (Hint: HS2)

Case

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 Study

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)

Quantitative Methods

Case Studies

Linear Programming

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

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

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 conometric 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

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

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

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

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.

Q2. What is the new super speed rail link between the north and south Britain called? (Hint: HS2)

CASE STUDY

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

Answer the following question.

Q2. What does MCDA stand for? (Hint: multi criteria decision analysis)

Linear Programming

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.

CASE STUDY

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

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 STUDY: 1

Question:

Calculate the probability.
In what situation does one need probability theory?
Define the concept of sample space, sample points and events in context of probability theory.
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:

Find the value of x.
In using regression analysis for making predictions what are the assumptions involved.
What is a simple linear regression model?

What is a scatter diagram method?

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 5^th year.

Question :

What is the Time Value of Money concept.
What do you mean by present value of money?
What is the Future Value of money.
What the amount to be credited at the end of 5^th

CASE STUDY : 4

Question:

What is most economical speed?
What is a chi-square test?
What is sampling and what are its uses.
Is there any alternative formula to find the value of Chi-square?

Quantitative Methods

Q1. 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

Q2. 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?

Q3. Calculate median from the following data:

Marks	10-25	25-40	40-55	50-70	70-85	85-100
Frequency	6	20	44	26	3	1

Q4. 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

Q5. 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?

Q6. In a binomial distribution 31% of the items are under 45 and 8% are over 64. Find the mean and variance of the distribution.

Q7. In a large number of group of children 55% are under 60 cm height and 40% are between 60 and 65 cm. Assuming a normal distribution, find the mean and SD of height

Q8. Construct index number from the data given by applying Marshall edge worthmethod.

Commodity	Price 2004	Quantity	Price 2006	quantity
A	2	8	4	6
B	5	10	6	5
C	4	14	5	10
D	2	19	2	13

QUANTITATIVE METHODS

What is model and give 4 examples . State their properties , advantages and limitation.
What are the types of inventories ? explain
What is replacement problem ? Describe some important replacement situation and policies ?
What is operation Research ? Account for the growing importance Research in business ?
Briefly discuss the Delphi method of making forecasts.
Define an OR model and give 4 examples. State properties, advantages & limitations
How do you distinguish between resource leveling and resource allocation problems? State and explain an algorithm for resource allocation.
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 TECHNIQUES IN MANAGEMENT

Q1. (a ) Define an OR model and give 4 examples.State properties ,advantages & limitations

(b) State the phases of an OR study and give their importance in solving problems

Q2. What is feasibility region ? is it necessary that it should always be a convex set ?

Q3. What are the types of inventories ? explain

Q4. What function does inventory perform ?

Q5. Briefly discuss the Delphi method of making forecasts.

Q6. What is MAD ? Discuss its importance in selection and use of forecasting models.

Q7. What is operation Research ? Account for the growing importance Research in business ?

Q.8 What is model and give 4 examples . State their properties , advantages and limitation.

Q9. What is a sequencing problem ? Explain and illustrate.

Q10. What is replacement problem ? Describe some important replacement situation and policies ?