A multistage stochastic programming approach in project selection and scheduling

In this paper, the joint problem of project selection and project scheduling under uncertain environment is formulated, analyzed, and solved by multistage stochastic programs. First of all, a general mathematical formulation which can address several versions of the problem is presented. A multi-period project selection and scheduling problem is introduced and modeled by multistage stochastic programs, which are effective for solving long-term planning problems under uncertainty. A set of scenarios and corresponding probabilities is applied to model the multivariate random data process (costs or revenues, available budget, chance of success). Then, due to computational complexity, a scenario tree of the resulted scenarios is constructed by scenario reduction algorithms. Finally, assuming resources of the projects to be limited and renewable, and present worth of profit of projects as the objective, the objective of the problem is maximized. Eventually, a case study is introduced and solved, and the results are presented. The effectiveness of the proposed algorithm is shown by the numerical results.