Multi-Criteria Decision Analysis: Key Concepts and Techniques

Sensitivity Analysis

2 Members of the Restrictions:

Sensitivity analysis is important because it allows us to determine the opportunity cost of resources.

Obtain Efficient Solutions

By optimizing one objective and considering the other as a parametric constraint, we can obtain an efficient solution for each value between its ideal and anti-ideal points of the objectives included as parametric constraints in the model.

Difference in Pairwise Comparisons in AHP and PROMETHEE

There are two types of pairwise comparisons in AHP: between criteria in the same level with respect to a criterion in the next higher level and between alternatives with respect to a criterion in the next upper level of the hierarchy. PROMETHEE is only based on pairwise comparisons between alternatives.

PROMETHEE requires us to know the behavior of the alternatives for each criterion quantitatively or qualitatively through the evaluation table. AHP only needs the relative contribution of an alternative over another with respect to a criterion, based on expert judgments.

Efficient Frontier in Efficient Portfolios

The efficient frontier shows the minimum risk of a portfolio, measured as standard deviation, for each value of the portfolio's total return.

Local Priorities

Local priorities are obtained from the pairwise comparison matrix when you compare criteria in the same level of the hierarchy with respect to a criterion in the next upper level or when you compare alternatives with respect to a criterion in the next upper level of the hierarchy.

Global Priorities

Global priorities are obtained by weighting the local priorities of the alternatives with the priorities of the criteria. They allow us to select and prioritize the alternatives in a decision problem.

Variance of Markowitz Model for Efficient Portfolios

Objectives of Investors

The values of the decision variables x_i (i = 1, 2... n) represent the proportion of each asset i in the portfolio. The objectives of investors are to maximize the expected return and minimize the total risk of the portfolio.

Expected Return

The expected return of a portfolio R(X) is the weighted sum of the individual average returns from the n assets that compose the portfolio, where the weights are the proportions of each asset, which are the decision variables of the model.

Risk of the Portfolio

The risk of the portfolio is measured by the variance of the portfolio's total return V(X).