Developing a Robust Multi-Skill, Multi-Mode Resource-Constrained Project Scheduling Model with Partial Preemption, Resource Leveling, and Time Windows

Real-world projects encounter numerous issues, challenges, and assumptions that lead to changes in scheduling. This exposure has prompted researchers to develop new scheduling models, such as those addressing constrained resources, multi-skill resources, and activity pre-emption. Constrained resources arise from competition among projects for limited access to renewable resources. This research presents a scheduling model with constrained multi-skill and multi-mode resources, where activity durations vary under different scenarios and allow for partial pre-emption due to resource shortages. The main innovation is the pre-emption of activities when resources are unavailable, with defined minimum and maximum delivery time windows. For this purpose, a multi-objective mathematical programming model is developed that considers Bertsimas and Sim’s robust model in uncertain conditions. The model aims to minimize resource consumption, idleness, and project duration. The proposed model was solved using a multi-objective genetic algorithm and finally, its validation was completed and confirmed. Analysis shows that limited renewable resources can lead to increased activity pre-emption and extended project timelines. Additionally, higher demand raises resource consumption, reducing availability and prolonging project duration. Increasing the upper time window extends project time while decreasing the lower bound pressures resources, leading to higher consumption and resource scarcity.