Value of information (VOI) is the amount a decision maker is willing to pay for information to better understand the uncertainty surrounding a decision, prior to making the decision. VOI is a key part of decision analysis (DA). Especially in this age of information explosion, evaluating information value is critical. VOI research tries to derive generic conclusions regarding VOI properties. However, in most cases, VOI properties rely on the specific decision context, which means that VOI properties may not be generalizable. Thus, instead, VOI properties have been derived for typical or representative decisions. In addition, VOI analysis as a method of DA has been successfully applied to practical decision problems in a variety of industries. This approach has also been adopted as the basis of a heuristic algorithm in the latest research in simulation and optimization. Portfolio Decision Analysis (PDA), rooted in DA, is a body of theories, methods, and practices that seek to help decision makers with limited budget select a subset of candidate items through mathematical modeling that accounts for relevant constraints, preferences, and uncertainties. As one of the main tools for resource allocation problems, its successful implementation, especially in capital-intensive industries such as pharmaceuticals and oil & gas, has been documented (Salo, Keisler and Morton 2011). Although VOI and PDA have been extensively researched separately, their combination has received attention only recently. Resource allocation problems are ubiquitous. Although significant attention has been directed at it, less energy has been focused on understanding the VOI within this setting, and the role of VOI analysis to solve resource allocation problems. This belief motivates the present work. We investigate VOI properties in portfolio contexts that can be modeled as a knapsack problem. By further looking at the properties, we illustrate how VOI analysis can derive portfolio management insights to facilitate PDA process. We also develop a method to evaluate the VOI of information portfolios and how the VOI will be affected by the correlations between information sources. Last, we investigate the performance of a widely implemented portfolio selection approach, the benefit-cost ratio (BCR) approach, in PDA practice. / text

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.