Project Portfolio Selection and Scheduling with Resource Allocation, Synergies, and Project Divisibility

A project portfolio can be defined as a set of project proposals that are selected according to one or more criteria by a decision-maker (individual or group). Regularly, the portfolio selection involves different decision problems, among those evaluation, selection, scheduling, and resource allocation. In published scientific literature, these problems have been addressed mainly separately giving as a result suboptimal solutions (portfolios). In addition, elements as partial allocation and project representation through tasks constitute relevant characteristics in practice that remain unaddressed in depth. The proposal of this research is to integrate the project selection and project scheduling, incorporating all relevant elements of both decision problems through the scheduling of tasks allowing to determine when the task will be funded and executed. The main impact of precedence rules at the task level in the portfolio is also studied. In this work, Project Portfolio Selection and Scheduling Problem (PPSS) is studied and solved through a new mixed-integer linear programming (MILP) model. The model incorporates renewable and nonrenewable resource allocation, along with partial and total funding policies, project divisibility, and interdependences. Scheduling is integrated into the model, both at the project level and at the project task level, which allows scheduling in noncontiguous periods. Small instances (up to 64 projects) and medium instances (up to 128 projects) were solved optimally in very short times. The relationship between the quality of near-optimal solutions and the solution computing time by modifying the parameters of the solver employed was researched. No significant change in the solution’s quality was perceived, but a significant reduction in solution computing time was achieved. Furthermore, the main effects of precedence rules on solution times and portfolio impact were studied. Results show that even if few precedence rules were introduced, the resource allocation of tasks changed significantly, even though the portfolio impact or the number of projects of the selected portfolios remains the same.

A scenario-based mathematical approach to a robust project portfolio selection problem under fuzzy uncertainty

As a major concern of chief managers in each organization, project portfolio selection has a special place in their responsibilities. To assist managers in making decisions, applicable optimization models play an essential role in such processes. In this regard, this paper provides a stochastic optimization model for a project portfolio selection problem under different scenarios. Providing the novelty in the model along with making it closer to reality, the interdependency between revenue and cost of projects is considered. Due to the inherent uncertainty of parameters, the revenue and cost of each project, as well as contributed capital, follow triangular fuzzy parameters. Contrary to the previous model, the appreciation of assets is considered in the proposed model as the other novelty of the proposed model. To tackle the uncertainty of parameters, a robust possibilistic approach is used, which has been first-ever devised in such problems. Being both optimistic and pessimistic approaches available for decision-makers, a new measure is introduced to make the model inclusive. Moreover, by considering the confidence level as both parameter and decision variables, the robust possibilistic programming approach is adopted to solve the proposed model. Using the new proposed measure, the optimal average value of robust model are obtained under different confidence level. Finally, solving the optimization model, the results are provided by implementing the realization for uncertain parameters, and regarding the obtained results, discussions are made to provide some insights to the managers.