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Learning Production Functions for Supply Chains with Graph Neural Networks
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Introduces temporal production graphs and an inventory module combined with temporal GNNs (SC-TGN, SC-GraphMixer) to learn hidden production functions and forecast supply chain transactions, plus an open-source simulator SupplySim.
Problem
Supply chain transaction graphs are governed by unobserved production functions that determine how firms transform inputs into outputs; existing temporal GNNs cannot learn these functions or use them for link prediction.
Approach
An inventory module tracks each firm's per-product inventory, updates it with bought amounts minus attention-weighted consumption, and learns production-function attention weights via an inventory loss with debt penalty and consumption reward; it is attached to temporal GNNs (extended TGN and GraphMixer for hyperedges and edge weights) and its debt penalties and caps inform edge prediction.
Key results
- Inventory module (emb) reaches MAP 0.262 on IED vs 0.127 for node2vec and 0.175 for PMI, learning production functions without observing them.
- SC-TGN+inv achieves MRR 0.540 on SS-std vs 0.441 for the strongest Edgebank baseline; SC-TGN reaches 0.820 on Tesla vs 0.507 for graph transformer.
- Across five datasets, the models outperform baselines by 11-62% on edge existence and 1-13% on edge weight; generated transactions under shocks keep AUROC above 0.93 seven timesteps ahead.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use product embeddings rather than directly learning inventory attention weights (ablation) | Inventory module · SS-std production learning | MAP: 0.771 (0.005) -> 0.790 (0.005) | Helped |
| Use product embeddings rather than directly learning inventory attention weights (ablation) | Inventory module · SS-shocks production learning | MAP: 0.770 (0.006) -> 0.778 (0.011) | Helped |
| Use product embeddings rather than directly learning inventory attention weights (ablation) | Inventory module · SS-missing production learning | MAP: 0.744 (0.006) -> 0.755 (0.007) | Helped |
| Use product embeddings rather than directly learning inventory attention weights (ablation) | Inventory module · IED production learning | MAP: 0.143 (0.004) -> 0.262 (0.005) | Helped |
| Add the inventory module to SC-TGN (ablation) | SC-TGN · SS-std future edge existence | MRR: 0.522 (0.003) -> 0.540 (0.003) | Helped |
| Add the inventory module to SC-TGN (ablation) | SC-TGN · SS-shocks future edge existence | MRR: 0.449 (0.004) -> 0.461 (0.009) | Helped |
| Add the inventory module to SC-TGN (ablation) | SC-TGN · SS-missing future edge existence | MRR: 0.494 (0.004) -> 0.494 (0.004) | No clear effect |
| Add the inventory module to SC-TGN (ablation) | SC-TGN · Tesla future edge existence | MRR: 0.820 (0.007) -> 0.818 (0.004) | No clear effect |
| Add the inventory module to SC-TGN (ablation) | SC-TGN · IED future edge existence | MRR: 0.842 (0.004) -> 0.841 (0.008) | No clear effect |
| Add the inventory module to SC-GraphMixer (ablation) | SC-GraphMixer · SS-std future edge existence | MRR: 0.453 (0.005) -> 0.497 (0.004) | Helped |
| Add the inventory module to SC-GraphMixer (ablation) | SC-GraphMixer · SS-shocks future edge existence | MRR: 0.426 (0.004) -> 0.448 (0.004) | Helped |
| Add the inventory module to SC-GraphMixer (ablation) | SC-GraphMixer · SS-missing future edge existence | MRR: 0.446 (0.003) -> 0.446 (0.002) | No clear effect |
Surprising findings
- Penalties and caps from the inventory module hurt edge prediction when transactions are missing, even with perfectly learned attention weights.
- Temporal correlation baseline is strong on standard synthetic data but degrades under supply shocks, while the inventory module is robust to delays.
Limitations
- Real TradeSparq data cannot be released, limiting replicability.
- Inventory penalties and caps are sensitive to missing transactions in the data.
- Assumes one production function per product (no firm-specific or substitute products).
Experimental setup
Datasets: Tesla (TradeSparq) IED (TradeSparq) SupplySim synthetic (SS-std, SS-shocks, SS-missing)
Benchmarks: Tesla IED SS-std SS-shocks SS-missing
Metrics: mean average precision (MAP) mean reciprocal rank (MRR) RMSE AUROC
Baselines: Edgebank Static embedding Graph transformer (UniMP) Temporal correlations PMI node2vec TGN (original)
Builds on: Temporal Graph Network GraphMixer Temporal Graph Benchmark UniMP ARIO model
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