Combining a multidimensional risk evaluation with an implicit enumeration algorithm to tackle the portfolio selection problem of a natural gas pipeline

Abstract

In pipelines, dealing with the dilemma of investing in a combination of the most critical sections without exceeding resources is a relevant issue. Some studies recommend using additive models with mathematical programming to solve portfolio problems, considering interval scale transformation. However, such a joint approach is inadequate when probabilistic consequences are used for evaluating a model based on Multi-Attribute Utility Theory (MAUT). Thus, it is not possible to ensure a better solution because the axiomatic structure of Utility Theory consequently prevents scale transformation. Therefore, this paper proposes a model to overcome bias in additive models for portfolio selection when an interval scale is the only form of measurement. Thus, a multidimensional risk evaluation is conducted and an implicit enumeration algorithm is used. A numerical application is applied to validate the proposed model, and a sensitivity analysis is conducted to verify its robustness. Results show that this model ensures a combination of sections with the highest values of aggregate risk, given the restrictions. Moreover, compared to the joint approach (without scale transformation), the proposed model also finds better solutions in over 99% of simulated cases. Furthermore, it can help managers effectively to allocate complementary resources to where they are most needed.