A Multi-Objective Portfolio of Portfolios Problem with Qualitative Performance Assessments

TL;DR

Addresses simultaneous selection of a portfolio of projects and portfolios of elements allocated to each project under multiple objectives, incorporating qualitative and quantitative criteria and feasibility thresholds involving decision variables $x_j$ and $y_{ij}$. Proposes an interactive MO-PoP framework that can be extended with temporal and stochastic uncertainty, using DRSA to elicit decision-maker rules that constrain the search over objective values $z_\ell$. Demonstrates via epsilon-constraint optimization and illustrative case studies how non-dominated portfolios are identified and refined through rule-based guidance, enabling DM-driven convergence to a satisfactory solution. The work offers a practical decision-support framework for complex, resource-sharing portfolio design with uncertainty and time, and outlines future directions including deck-of-cards preference elicitation and exact Pareto-front representations.

Abstract

We present a multi-objective portfolio decision model that involves selecting both a portfolio of projects and a set of elements to allocate to each project. Our model includes a defined set of objectives to optimize, with projects contributing to these objectives in various ways. The elements included in the portfolios are assessed based on both qualitative and quantitative criteria. Projects can only be selected for the portfolio if they meet specific requirements defined by threshold values on the criteria. The model is adaptable to include temporal considerations and stochastic, making it suitable for a wide range of real-life applications. To manage the decision-making process, we employ an interactive multi-objective method that integrates the selection of both portfolios and elements. After making initial selections, we ask the decision-maker to evaluate the portfolios, from which we derive a series of rules to be incorporated into the multiobjective model until the decision-maker is satisfied. We illustrate the functionality of our model through an illustrative case study.