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Quantitative Methods
Multi Criteria Decision Making (20 Marks)
MCDA. (multi criteria decision analysis) is considered to be one of the fastest growing research operations in the last several years. The researcher focus towards MCDA led to development of many different approaches and ways in the field. There are two types of procedures: theoretical assumptions and decision addressed type. This difference throws challenges to the prcedure of choosing the most ideal method for the decision making problem. Most of the time, the initial approach towards applying MCDA in the real world problems relates to the set up of simple understanding Of the context and recognizing the problem of decision. This step includes the ones• who make decisions and other important participants who make important contributions for the MCDA procedure by sharing their knowledge. The common insight of the decision framework is received by knowing the goals of the decision making body and recognizing not only those people who make decisions but also those who face the decision. • Dooley (2009) says that the first three steps take up more time in the process of MCDA, particularly because of their qualitative features. Assigning of comparative significant weights to the selected criteria is the next step: These weights can be ascertained directly, for example ranking, swing, trade off; or indirectly, for example centrality, regression and interactive. Later, the DM has to give individual scores, considering his or her views, to each of the recognized options according to the criteria which seem vital. These scores show the decision of DM . related to spreading of each substitute to every performance standard. The information which is attained is maintained distinctively into performance template, which is also as consequence matrix, options matrix, or just decision table. The next process includes abstract of the information consisting of the performance matrix in the form of multi criteria scores, for every possible plan. Mostly, this is attained by combining the individual scores of matrix so that total valuation of .each substitute which allows more comparison. The groups of substitute ranked on the basis of all these scores. Finally, the procedure can include a warm evaluation of
the outcome to amendments in the scores or criteria, to conclude the sturdiness of the result of MCDA. At the end, the analysis and trade offs included in the respective choices are given to and conferred with the DM. In many cases, the ultimate decision that DM takes, does not match with the highest level of alternative, as they are more focused towards the process of knowing the effect each and every factor in ranking of choices than in the exactness of the ranking. Also, it should be observed that the generalizations are not used to of the outcome given by the process of MCDA, and they only appropriate for the group of choices which were assessed.
Answer the following question.
Q1. What role does MCDA play in decision making? (Hint: MCDA is considered to be one of the fastest growing research operations, these scores show the decision of DM related to spreading of each substitute to every performance standard)
Q2. What does MCDA stand for? (Hint: multi criteria decision analysis)
A monte Carlo Case Study (20 Marks)
Laura,' a 57 year old unmarried woman, earns around 68,000 dollars per year with expenditure of 37,500 dollars. She hit away 14,000 dollars each year and collected 330,000 dollars in her RRSP and TFSA, and also a rented apartment worth 250,000 dollars. She has a iixed pension given by her employer, although it is not indicated to price rise, and Is entitled to get complete benefits of 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 the best 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 suppositions 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)
CASE STUDY (20 Marks)
The cost of fuel in running of an engine is proportional to the square of the speed and is Rs 48 per hour for speed of 16 kilometers per hour. Other expenses amount to Rs 300 per hour. What is the most economical speed?
Answer the following question.
Q1. What is most economical speed?
Q2. What is a chi-square test?
Q3. What is sampling and what are its uses.
Q4. Is there any alternative formula to find the value of Chi-square?
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?
Assignment Solutions, Case study Answer sheets
Project Report and Thesis - Contact
ARAVIND – 09901366442 – 09902787224
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