Simulation-based hybrid genetic algorithms for the stochastic multi-mode resource-constrained project scheduling problem with minimized financial risk

Projects face uncertainties during implementation, and these uncertainties often lead to risk factors that disrupt successful project execution and cause a loss of profit. The stochastic project scheduling technique has been an effective avenue for reducing the risks in project management. Nevertheless, previous studies often neglected resource limits for minimizing the financial risks of projects in stochastic project scheduling problems. This study aims to optimize the conditional net present value at risk (CNPVaR), which measures a project's expected loss of net present value (NPV) in a stochastic multi-mode resource-constrained project scheduling problem (SMRCPSP). Accordingly, considering the stochastic activity duration and cash flow, we construct a scenario-based optimization model for the SMRCPSP, where the solution (strategy) of the SMRCPSP is represented by a policy that includes an activity list and execution mode list; a scheduling policy is then employed to map the start times of activities at each decision time based on the solution. Three simulation-based hybrid genetic algorithms embedded with different iteration alternatives according to activity-based (AB) or resource-based (RB) scheduling policies are used. Furthermore, computational experiments are conducted to evaluate the proposed procedures through 480 instances. With respect to the CNPVaR, expected NPV, and algorithm stability metrics, the results of the experiments demonstrate that the genetic algorithm (GA) with local search based on the RB scheduling policy performed best compared with two other hybrids of the GA, the existing vibration damping optimization (VDO) method and a pure GA for large-sized projects. However, the VDO outperforms the other approaches according to the AB scheduling policy for small-scale projects. Additionally, a case study is conducted; the findings demonstrate that the risk attitude (confidence level) of project managers and the discount factor have impacts on the CNPVaR and expected NPV, but the CNPVaR is insensitive to the number of simulations.