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This paper presents a novel formulation of the integrated bi-objective problem of project selection and scheduling. The first objective is to minimize the aggregated risk by evaluating the expected value of schedule delay and the second objective is to maximize the achieved benefit. To evaluate the expected aggregated impacts of risks, an objective function based on the Bayesian Networks is proposed. In the extant mathematical models of the joint problem of project selection and scheduling, projects are selected and scheduled without considering the risk network of the projects indicating the individual and interaction effects of risks impressing the duration of the activities. To solve the model, two solution approaches have been developed, one exact and one metaheuristic approach. Goal Programming method is used to optimally select and schedule projects. Since the problem is NP hard, an algorithm, named GPGA, which combines Goal Programming method and Genetic Algorithm is proposed. Finally, the efficiency of the proposed algorithm is assessed not only based on small size instances but also by generating and testing representative datasets of larger instances. The results of the computational experiments indicate that it has acceptable performance to handle large size and more realistic problems.

Integrated bi-objective project selection and scheduling using Bayesian Networks: A risk- based approach