A mathematical model for project portfolio selection with project interdependency, project divisibility, reinvestment and resourcing in different ways

Project portfolio management consists of repetitive cycles of project evaluation, selection and execution. Project portfolio selection is the main part of project portfolio management. Organization identifies and prioritizes projects that are mostly aligned with stated strategic goals while considering real-world restrictions and considerations that are related to scheduling and resource allocation. In this paper, a new comprehensive model for the project portfolio selection problem over a planning horizon with multiple periods by maximizing profit is developed in which simultaneous selection, scheduling and resource allocation of projects are considered. The model incorporates project interdependency and strategies of project divisibility, reinvestment, external investment and resourcing in different ways at the same time in choosing the best execution schedule for the projects in real-life applications. In addition, resource and budget constraints, cardinality restriction, precedence relationship and scheduling, setup and resource costs are included in the model. Numerical examples under eight scenarios are presented to highlight the characteristics of the proposed model.