project networks with graph neural networks
Predicting project duration and cost from activity–resource graphs, beyond CPM and PERT.
CPM and PERT have been the default tools for project scheduling for six decades. Both rest on assumptions that are convenient rather than true: that task interdependencies are static, and that a resource performs the same way regardless of what else it is assigned to. Real projects violate both constantly.
Modelling projects as graphs
We represent a project as a heterogeneous graph with two node types — activities and resources — and edges carrying precedence, assignment, and contention relationships. This lets the model see that two activities compete for the same crew even when there is no precedence arc between them, which is exactly the structure a critical-path calculation throws away.
Two architectures were evaluated:
- GraphSAGE, for the static case, aggregating over sampled neighbourhoods so the model scales to large project networks.
- Temporal Graph Networks, for the case where the graph itself evolves as the project progresses and resources are reassigned.
Results
Against conventional statistical baselines, the learned models reduced mean absolute error on duration and cost prediction by 23–31%, with R² reaching approximately 0.91 on the more complex project networks.
Just as usefully, the learned node embeddings turned out to be interpretable: resources whose embeddings drifted furthest from their initial position were consistently the ones acting as bottlenecks, and activity embeddings clustered around the genuine critical dependencies rather than the nominal critical path.
The preprint (Mirjalili et al., 2025) is on arXiv, joint work with Behrad Braghi and Shahram Shadrokh Sikari.