A Hybrid Multi-Population Approach to the Project Portfolio Selection and Scheduling Problem for Future Force Design

Abstract

Future Force Design (FFD) is a strategic planning activity that decides the programming of defence capability options. This is a complex problem faced by the Australian Department of Defence (DoD) and requires the simultaneous selection and scheduling of projects. Specifically, this is a NP-hard problem known as the Project Portfolio Selection and Scheduling Problem (PPSSP). While the PPSSP is a complex problem itself, its complexity is further increased when coupled with the additional characteristics that arise in the context of defence-oriented planning, such as long planning periods and complex operational constraints. As a result, many previous studies examined only a small number of projects over a short planning period and are largely unsuitable for the scale required in the defence sector. To address this issue, two primary contributions are made in this paper. Firstly, this study describes a complex practical PPSSP, inspired by the FFD process, and develops a corresponding mathematical model. Problem instances are derived from real-world, publicly-available defence data. Secondly, to address instances of the problem, two existing meta-heuristics are considered and a hybrid, multi-population approach is proposed. Results are compared against those attained by a commercial exact solver and indicate that there is no statistically significant difference in performance between the proposed multi-population approach and the exact solver. A key benefit of the proposed meta-heuristic approach is that its run time is not significantly influenced by the complexity of the problem instance. Additionally, many interesting practical insights regarding the solution of selection and scheduling problems are uncovered.