A community detection approach for the resource leveling problem in a multi-project scheduling environment

This paper develops an integrated mathematical formulation that embraces the Resource Leveling Problem (RLP) and the Multi-Project Scheduling Problem (MPSP). To incorporate both aspects into one formulation, the proposed model is bi-objective that seeks to minimize projects' durations and resource usage, simultaneously. Resources are not available in all time periods because of sickness, failure, maintenance, holidays, training, laying off, etc. This assumption complicates the scheduling process for multiple concurrent projects that share a limited number of resources with finite capacities. To tackle this intricacy, a coherent approach is required that not only schedules activities of multiple projects, but also levels resource consumptions as efficient as possible. Therefore, this study offers an approach based on the Community Detection problem to identify homogeneous communities of activities that have common resource requirements. These communities are obtained by the Vibration Damping Optimization (VDO) method through modularity maximization. The identified communities help the projects' planner to avoid simultaneous scheduling of the activities within a community; hence, resource consumptions are minimized. A Multi-Objective Gravitational Search Algorithm (MOGSA) is developed to solve the proposed bi-objective problem. The MOGSA uses the communities detected by the VDO and schedules the projects. The MOGSA has been invigorated by using two Cellular Automata (CA), namely "Seeds" and "Wolfram's elementary cellular automaton" in its procedures. A set of test problems have been examined to compare the efficacy of the MOGSA with some of the best existing algorithms. The results demonstrate that the MOGSA is highly competitive and yields proper solutions comparing to the outputs of well-known optimizers. Besides, a real construction case study has been presented to demonstrate that the proposed model and algorithm can deliver practical solutions.