Multi-mode resource-constrained project scheduling problem with viability approach

This study aims to introduce the Viability approach for a Multi-Mode Resource Constrained Project Scheduling Problem (VMRCPSP) that integrates sustainability, agility, and resilience to improve its effectiveness. Therefore, we address a gap in the RCPSP by proposing a new mathematical model that focuses on a relatively underexplored area. This method is groundbreaking in RCPSP, as it employs MILP, robust stochastic programming, and MAD as a risk criterion to reduce disruption risk. A viability approach that incorporates multi-mode and resource constraints enhances project performance. Two models, VMRCPSP and MRCPSP, were compared, revealing that VMRCPSP outperformed MRCPSP in terms of total cost, emissions, and energy at the start of the final task, with an average gap of −1.4%. Sensitivity analysis showed varying disruption rates increased costs and emissions without affecting computation time. Adjusting confidence levels also raised total costs and emissions, while disruptions in task duration reduced costs and emissions. Additionally, increasing the problem scale raises costs, emissions, and computation time, suggesting the need for advanced algorithms to manage large-scale issues better.