A comprehensive mathematical model for resource-constrained multi-objective project portfolio selection and scheduling considering sustainability and projects splitting

Abstract

In the portfolio project selection problem with budgetary and resource constraints, it is frequently assumed that projects cannot be interrupted and can be merely scheduled and processed in consecutive time periods in which resources have been sufficiently allocated. Due to improvement in consuming resources and budgets, this study addresses a linear multi-objective for sustainable project portfolio selection problem that allows projects to be split at any time and postponed to be re-executed at another time. Furthermore, due to the importance of sustainability in projects, the aim of this model is selecting and scheduling projects according to criteria of the sustainability balanced scorecard, time-dependent criteria, resource, and budget constraints. For that reason, a hybrid multi-criteria decision-making approach is considered for ranking, scoring and calculating the sustainable utility of projects. Then, the proposed model is interpreted as a multi-objective optimization where the total benefits and the value of utility for projects are maximized, and the summation of the absolute amount of interruption in executing the selected projects is minimized. In addition to the constraints of budget and resources, and considering the conflicting projects, a novel mathematical formulation is presented to employ the dependency relationship between some projects in both processes of selecting and scheduling the projects. In order to validate this model, several numerical case studies are provided and solved by the ε-constraint method under various circumstances, including un-splitting projects with unlimited resources, constrained resources, splitting projects and interpretation of multi-objective problem. Finally, their results are analyzed and investigated. The results demonstrate that more benefits will be obtained when projects have permission to be split. However, increasing the sustainability of projects and reducing the risk of interruption should not be overlooked, which is why they have been explored as the objective functions in other numerical case studies.