Resource allocation and Uncertainties: An application case study of portfolio decision analysis and a numerical analysis on evidence theory

The thesis is divided into two parts concerning different topics. The first is solving a multi-period portfolio decision problem, and the second, more theoretical, is a numerical comparison of uncertainty measures within evidence theory. Nowadays, portfolio problems are very common and present in several fields of study. The problem is inspired by a real-world infrastructure manage- ment case in the energy distribution sector. The problem consists of the optimal selection of a set of activities and their scheduling over time. In scheduling, various constraints and limits that the company has to meet must be considered, and the selection must be based on prioritizing the activities with a higher priority value. The problem is addressed by Port- folio Decision Analysis: the priority value of activities is assigned using the Multi-Attribute Value Theory method, which is then integrated with a multi-period optimization problem with activities durations and con- straints. Compared to other problems in the literature, in this case, the ac- tivities have different durations that must be taken into account for proper planning. The planning obtained is suitable for the user’s requirements both in terms of speed in providing results and in terms of simplicity and comprehensibility. In recent years, measures of uncertainty or entropy within evidence theory have again become a topic of interest in the literature. However, this has led to an increase in the already numerous measures of total uncertainty, that is, one that considers both conflict and nonspecificity measures. The research aims to find a unique measure, but none of those proposed so far can meet the required properties. The measures are often complex, and especially in the field of application, it is difficult to understand which is the best one to choose and to understand the numerical results obtained. Therefore, a numerical approach that compares a wide range of measures in pairs is proposed alongside comparisons based on mathematical proper- ties. Rank correlation, hierarchical clustering, and eigenvector centrality are used for comparison. The results obtained are discussed and com- mented on to gain a broader understanding of the behavior of the measures and the similarities and non-similarities between them.