SECTION A

INTRODUCTION

Decision-making is a structured process which involves looking out for the best possible alternative available from the list of options. It is crucial for every individual to make rational decisions in every aspect of life and ensure they are free from any bias. This decision-making has an impact on individuals, private organizations, public sector Organizations and society. For individuals, it can be a decision based on the choice of a course at a university; a private Organization would have to choose a suitable delivery service to ensure the product reaches the customers; the public sector, either the local authorities or national government make decisions like offering a grant, adopting a new local plan, opening a new school or offering a contract after a tender process. Likewise, society would have to make decisions based on the impact of activities affecting climate change.

If one considers decision-making, it is important to know that there is no specified format or solution to the various decision-making problems. Decision-making aims at helping individuals make decisions based on their understanding which would help them justify their choice of action.

Decision of one can be dissatisfactory to another. It should be understood that the method opted for decision-making to enable the decision maker make better decisions.

In the field of decision-making, including the concept of priority is quiet important and how the priorities have been derived influences the choice that an individual makes (Saaty, 2003).

The rationality involved in the decision-making process has been simplified by the use of the various techniques that have been developed in the past decades. One such process is the Analytic Hierarchy Process (AHP) used in addressing problems arising out of decision-making. AHP is a theory of relative measurement of intangible criteria (Figueria, Greco, & Ehrgott, 2005).

This decision-making work applies to use of AHP to make a decision in the selection of a house to buy from the 7 alternatives available. Based on the various criteria adopted for this decision-making process, the outcome is expected to help decide which house is the best option to buy.

LITERATURE REVIEW

Analytical Hierarchy Process was developed by Saaty (1977, 1980). It is useful when the decision maker is unable to construct a utility function (Ishizaka,Nemery, 2013).Just like any MCDA method, the problem needs to be structured. Scores are calculated based on the pairwise comparison that are provided by the user. There are two additional steps needed to complete AHP which are consistency check and Sensitivity analysis. (Ishizaka,Nemery, 2013)

AHP is based on the rule of divide and conquer as it is an advantage to solve one sub-problem at a time. The breakdown of the process consist of 2 stages namely Problem structuring and “elicitation of priorities by pair-wise comparison” (Ishizaka, Nemery, 2013).

AHP provides an easy platform to compare the various alternatives and arrive at making the choice. It can be easily understood and is less complex when compared to the other MCDA techniques. AHP is a structured process with 3 different levels. The first level represents the goal. The second level represents the criteria used to make the decision and level 3 represents the alternatives. The above three levels are essential to solve a problem using AHP. The output of AHP consists of mathematical weights that reflect the relative importance of each criterion when compared against the other criteria (Hoffman, Schniederjans, Sirmans, 1995).

TABLE 1: PROBLEM STRUCTURING

Table 1 shows the Problem structuring that would be used to make a decision using AHP (Expert Choice). The model in Table 1 is categorized into 3 different levels namely Level 1,2 and 3.

LEVEL 1: This level defines the goal of the model which relates to buying of a house.

LEVEL 2: This level defines the criteria based on which the user will base his decisions on. (Appendix 1)

LEVEL 3: This level defines the possible outcomes of the alternatives which is whether to buy the house or not and which house would make the best chance of being selected.(Appendix 2).

Table 2 shows the Description of the Model where various criteria are used to make a selection. A customer always looks for a perfect mix or combination of facilities. If the buyer finds what he is looking for, he would not mind paying a little extra to get the best available option.

PROBLEM SOLVING

Expert choice has been used to make a selection of the best alternative from the list of alternatives (Appendix 3)

ANALYSIS OF RESULTS AND RECOMMENDATIONS

Based on the ranks assigned to the various houses, It can be noted that House 4 is the best possible alternative which the decision maker will select (Appendix 4).It is recommended that the buyer also study other factors before buying a house (Appendix 4).

CONCLUSION

In summary, AHP helps a decision maker make a rational choice from the various alternatives available. The user is more likely to weigh his options based on which he would make decisions. Decisions vary from person to person and the criteria given the maximum weight are solely based on the decision maker.

Here it can be noted that based on the analysis, Price was considered the most important criteria and a decision maker’s buying capacity is based on his income and which is why the cost has a big impact. This may not be the same for all as there are possibilities where there exist some individuals where price is not a major concern.

SECTION B

A) CONSTRUCTION OF A HISTOGRAM TO SHOW THE DISTRIBUTION OF ANNUAL RETURN

HISTOGRAM SHOWING THE DISTRIBUTION OF ANNUAL RETURN

B) DISCUSSION IF THE DISTRIBUTION IS NORMAL

Normal Distribution 1SD above and below mean

About 68.3% of Annual returns lie within one standard deviation from the mean Annual Return as shown in the graph above.

Normal Distribution 2SD above and below mean

About 95.4% of annual Return lies within two standard deviation from the mean annual return as shown in the graph above.

Normal distribution 3SD above and below mean

About 99.7% of annual Return lies within three standard deviation from the mean annual return as shown in the graph above.

Therefore it can be stated that the above distribution is a normal Distribution as it satisfies the Normal distribution estimates.

C) CALCULATION OF THE QUARTILES

Lower Quartile = 60.5.

Interpretation: 25% of the funds have less than 60.5% annual return, that is, out of 10 funds, 2.5% of the funds are below 60.5% Annual Return.

Inter-quartile range = 15

Interpretation: By disregarding the lower 25% and upper 25% of the spread of funds, the cumulative difference of the funds within the 50th percentile cumulative difference is 15. Average difference in spread of the funds in 50th percentile is 2.5%which is lower than the difference in the first and third quartile which is 59-54 and 83-79.This means that the spread is close to the funds within the 50th percentile.

The difference between the funds is not so significant.

D) CORRELATION COEFFICIENT

The approximate value of Correlation Coefficient

Kendall’s Correlation coefficient

In the above table (Kendall’s Correlation Coefficient), the figure (-1) implies that the association between the 10th and the 1st observation in the table is negative. This means the higher value of a variable is associated with the lower value of another variable.

In the above given scenario, the 10th observation has the highest annual safety rating (7.2 as opposed to 7.1) but the lower annual return. This shows that if two variables are considered in isolation to study the relation between them, then there is a negative correlation between Annual safety rating and Annual Return.

PEARSON CORRELATION COEFFICIENT

Pearson’s correlation coefficients range from -1 to +1. The correlation coefficient of -0.736736 means there exists a strong negative correlation between annual Safety Rating and Annual Return which means that higher Annual return, lower the Annual Safety Rating and lower the Annual return, higher the Annual Safety Rating.

E) CALCULATION OF STANDARD DEVIATION OF ANNUAL SAFETY RATING

Standard Deviation is used to measure how dispersed the data is from the mean. The closer the value to the mean, the smaller the deviation and vice-versa.

In the data represented above, the standard deviation is 0.3411 which means that the data is closer to the mean of 6.94. This signifies that the standard deviation from the mean is small (0.3411)

REGRESSION ANALYSIS

F) CALCULATION OF ESTIMATED ANNUAL RETURN FOR THE FUND

G) CONCLUSIONS FROM THE REGRESSION ANALYSIS ABOUT THE EFFECT OF ANNUAL SAFETY RATING AND EXPENSE RATIO ON ANNUAL RETURN

From the above regression analysis on the effect of Annual safety Rating and Expense Ratio on Annual Return, it can be concluded that for every unit of Annual Safety Rating used to predict the Annual Return, it will have a negative impact of -15.36839259. On the other hand, for every unit of Expense ratio used to predict annual Return, it will have a positive impact of 13.55832143%.

For every unit added or subtracted from the Annual Safety Rating, there would be a corresponding negative impact of -15.368 on the Annual Return.

For every unit added or subtracted from the Expenses Ratio, there would be a positive impact of 13.5583% on the Annual Return.

H) R SQUARE VALUE

R-square is also known as the co-efficient of determination indicates how accurate and precise the predicted profits are most likely to be. An R square value of 1 indicates suggests a complete accurate prediction. A value of 0 indicates the model is of no help to predict profits. With an R² of 0.696306177, it is possible to say that the regression model is strong enough to predict future annual return by taking into consideration Expense Ratio and annual Safety Rating ( also refer Table 12).

I) P-VALUE NUMBER IN THE REGRESSION OUTPUT

The number is used to determine whether or not to accept or reject the null hypothesis for each independent variable.

Annual Safety Rating with a p-value of 0.033514 is significant at 5% significance level thereby resulting in rejecting the null hypothesis (H0) which says there is a relationship between Annual Safety Rating and Annual return and to accept the alternative hypothesis (H1) which states that relation between Annual Safety Rating and annual Return exist.

Expense Ratio with a p-value of 0.0101994 is not significant at 5% significance level, thereby resulting in rejecting the Alternative hypothesis (H1) which says there is no relationship between the Annual Return and the Expense Ratio and accepting the Null Hypothesis (H0).

Intercept with a p-value of 0.012022 is significant at 5% significance level thereby resulting in rejecting the Null Hypothesis ( H0 ) which states there is a relationship between the intercept and Annual return and to accept the Alternative Hypothesis ( H1 ) which states that relationship between Annual Return and Intercept exist.

None of the p-value is significant.

At 1% significance level intercept of 0.012022, Annual Safety Rating 0.033514 and Expense Ratio of 0.101994 are not significant resulting in accepting the Null hypothesis (H0 ) which says there is no relationship between the three and to reject the Alternative Hypothesis (H1 ).

The impact of a lower p-level is that the confidence level is 99% to the extent of which none of the independent variables is reliable enough to predict the dependent variable.

J) BENIFITS AND DIFFICULTIES OF MUTIPLE REGRESSION

Multiple regression studies the relationship between the dependent variable and the numerous independent variables. Multiple Regression helps determine the relative influence of one or more independent variables to the criterion. It also helps identify any abnormalities. Monte Carlo simulations generate multiple graphs unlike in the Deterministic models which enables easy understanding of the information by stakeholders.

Every method has its pros and cons. Likewise, multiple regression has its disadvantages too. The use of the regression model is usually based on the data being used. Use of incomplete, inaccurate or false data can affect the accuracy of the analysis. It is difficult to use the multiple regression analysis using one constant variable against a list of independent variables. Casual deductions cannot be drawn from this analysis because it is based on the correlation between the different variables. The inclusion or exclusion of a predictor variable can, the contributions of that predictor variable in the analysis is most likely going to change.

K) RECOMMENDATIONS

Multiple Regression is used to improve the prediction power of the regression model for the purpose of obtaining a dependent variable.

For further analysis, it is advised to run a simple regression on each independent variable and decide which of the independent variable is reducing the predicting power of the multiple Regression Model. Though the simulations would enable the company to arrive at a conclusion, certain qualitative factors like work ethics, corporate governance and quality of the product should be taken into consideration to make sound decisions.

SECTION C

MONTE-CARLO SIMULATION

A) ESTIMATION OF EXPECTED MONETARY VALUE FOR EACH PRODUCT

The above table represents the Expected Monetary value for three 3 products on behalf of AJS Ltd.

In the above tabulated data, the expected monetary value for each product is arrived at by multiplying the demand for each product with the probability of demand of the product. The resulting figure is the Expected demand. The same is to be carried out for the different categories.

B) TABLE 2: Calculation of Profits

TABLE 3: Data used to run the Monte-Carlo Simulation

TABLE 4: Calculation of Variable Cost

TABLE 5: Calculation of machine Failure

MONTE CARLO SIMULATED GRAPHS

Graph 1, 2 and 3 are generated before running the Monte-Carlo simulation.

GRAPH 1: Product 1

C) RECOMMENDATIONS TO THE MANAGEMENT

From the various computations on the three products, Product 3 has the highest profit generating capacity when compared with Product 1 and 2. Before running the simulations, it can be noted that Product 3 generated the highest profits (Table 2, Graph 1,2 and 3) than Product 1 and 2 with the machine failure and Variable cost remaining constant. This wouldn’t suffice to give recommendations since the costs tend to fluctuate.

After running the simulations it can be noted that product 3 has the maximum profit earning capacity at 89.1% by generating a maximum profit of 175,492 as opposed to the maximum profits generated by product 1(89,552) and Product 2 (128,964) at the same capacity.

Variable cost and machine failure are the two major costs that could have an impact on the profit generating capacity of the Products. These costs tend to fluctuate based on the load, the usage of machine and any additional costs being incurred to benefit the process of production. Certain costs are inevitable and need to be borne by the management so as to benefit the smooth functioning of the department and the Organization as a whole.

The management needs to be aware that these additional costs could have an impact on the profit generated. To reduce the possibility of incurring unwanted or unexpected costs, the management should ensure that trained technicians operate the machinery. Proper training must be given to all the operators involved in handling the machinery.

An appropriate depreciation policy would have to be adopted. By doing so, the Organization can try to cover the fixed cost of the asset before its useful life and can also create funds to replace the asset in future.

The management should have an Asset replacement policy in place to ensure that there is an optimal mix based on t asset being used and its usage. This also helps management decide the desired or accepted level of risk that can be undertaken.

If an amount is invested in training operators and the other costs mentioned above, it does not mean that the production process of product 3 has been made more expensive, rather it has just increased the fixed cost element which would have been incurred even without producing the product. This can be explained using the Price-sensitivity analysis. It can be said that companies are less price sensitive since they look for good quality of product/services and are more focused on the long term benefits than short-term.

D) ADVANTAGES OF USING MONTE-CARLO SIMULATION OVER DETERMINISTIC ANALYSIS

§ The probabilistic output shows the feasibility of each output and not just what could happen.

§ It is easy to generate graphs for the different outputs and their likelihood of occurrence which is essential in communicating results to stakeholders.

§ Monte Carlo analysis promotes the understanding of the effects of the various inputs on the output.

§ By applying Monte Carlo simulation, the management can clearly see which inputs carried which values when certain outcomes were generated. This is crucial for the future production and analysis. In deterministic models, it is very difficult to model different combinations of values for different inputs.

§ It is possible to model interdependent relationships between input variables.

§ The knowledge level of mathematics required for understanding the process is basic.

§ Monte-Carlo Simulation can help automate the tasks involved.