Project selection and scheduling for phase-able projects with interdependencies among phases

This research proposes a model for project selection and scheduling when some of the projects in the available pool of projects can be implemented in phases. We present a mixed integer programming (MIP) model that maximizes the Net Present Value (NPV) of future investments in situations where temporal budget limitations and reinvestment strategies exist. The MIP reveals the optimal phasing solution. It models the Interdependencies among different phases of a project and also takes the foundation/infrastructure requirements for development of future phases into consideration. To solve large-size problems, we present a solution method that initially reduces the problem size. Then, a two-step heuristic is presented that in the first step adds projects to the pool of selected projects one by one based on a favorability measure and in the second step, eliminates some phases of the chosen projects with some probability. The performance of the heuristic is illustrated through five small-size and four large-size examples. We perform sensitivity analysis by altering various parameters that affect the heuristic's performance such as different favorability measures, and different initial available budgets. The results are favorable for the preprocessing step and solution heuristic. On small-size scenarios, the heuristic can find the optimal solution from the MIP in almost all cases. Furthermore, on large-size scenarios, the heuristic finds solutions within approximately 100 s that are better than the ones found by solving the MIP given a 10,000 s time limit.