Multi-phase Projects Selection and Scheduling Problem: A Multi-objective Optimization Approach

At the management level of project-based and construction organizations, choosing an optimal portfolio of projects is one of the most strategic and vital decisions. This research model the hybrid problem of selecting the optimal project portfolio and scheduling activities considering resource and budget constraints. Therefore, a two-objective mixed-integer nonlinear programming model is presented that enables the selection and scheduling of phased projects. The model objective functions include maximization of the net present value and minimizing the variance of renewable resources that perform resource-leveling. The proposed model has solved using two methods; augmented epsilon constraint and a meta-heuristic genetic algorithm based on non-dominated sorting. A set of Pareto front results derived from these two methods using the Pareto front distance, variation, and non-uniformity criteria were compared and evaluated. The results revealed that the augmented epsilon constraint method provided more favorable results and better efficiency in small-scale instances. By comparing the results of two methods of augmented epsilon-constraint and genetic algorithm in an example with five projects, six phases, and five time horizons (N5M6T5) showed that the NPF and NPS criteria in the augmented Epsilon constraint method are less than them in the genetic algorithm method and the DM and S criteria are more in the genetic algorithm method than them in augmented Epsilon constraint method. For large-scale problems, the genetic algorithm finds the Pareto front of the problem practically in less time. The most important practical application of this research is for project-based companies that seek to choose and schedule several projects. For these companies, the results of this study help to reduce the tolerance of using resources and increasing their profits.