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Time Series Supplier Allocation via Deep Black-Litterman Model
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Proposes DBLM, a deep Black-Litterman model that uses an STGNN to learn perspective matrices for time series supplier allocation, trained with a masked Spearman rank loss.
Problem
Time series supplier allocation (TSSA) requires allocating orders across suppliers to balance demand satisfaction against shortage-of-supply risk, but the Black-Litterman model relies on handcrafted perspective matrices and lacks supervision and reliable data.
Approach
Adapts the Black-Litterman model to supply chains by learning the perspective matrix and error covariance from spatio-temporal features (ChebGCN + TCN with attention fusion), supervised by a masked Spearman rank correlation loss that ignores unengaged suppliers.
Key results
- On MCM-TSSA, DBLM reaches HR@50 of 0.487 and MRE of 0.518, outperforming the best baseline ECM (HR@50 0.348, MRE 0.641).
- On SZ-TSSA, DBLM achieves HR@50 of 0.662 and MRE of 0.327 versus ECM's 0.412 and 0.493.
- Ablation shows removing the BL component causes the largest performance drop among the variants.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the BL component instead of using Markowitz weights (ablation) | DBLM · MCM-TSSA | HR@50: 0.347$\pm$0.529 -> 0.487$\pm$0.356 | Helped |
| Add the BL component instead of using Markowitz weights (ablation) | DBLM · SZ-TSSA | HR@50: 0.325$\pm$0.431 -> 0.662$\pm$0.182 | Helped |
| Use the STGNN encoder rather than an MLP (ablation) | DBLM · MCM-TSSA | HR@50: 0.377$\pm$0.340 -> 0.487$\pm$0.356 | Helped |
| Use the STGNN encoder rather than an MLP (ablation) | DBLM · SZ-TSSA | HR@50: 0.420$\pm$0.170 -> 0.662$\pm$0.182 | Helped |
| Add the TCN encoder (ablation) | DBLM · MCM-TSSA | HR@50: 0.393$\pm$0.342 -> 0.487$\pm$0.356 | Helped |
| Add the TCN encoder (ablation) | DBLM · SZ-TSSA | HR@50: 0.448$\pm$0.240 -> 0.662$\pm$0.182 | Helped |
| Add the DGCN encoder (ablation) | DBLM · MCM-TSSA | HR@50: 0.431$\pm$0.330 -> 0.487$\pm$0.356 | Helped |
| Add the DGCN encoder (ablation) | DBLM · SZ-TSSA | HR@50: 0.473$\pm$0.150 -> 0.662$\pm$0.182 | Helped |
| Add fusion attention rather than directly combining embeddings (ablation) | DBLM · MCM-TSSA | HR@50: 0.453$\pm$0.328 -> 0.487$\pm$0.356 | Helped |
| Add fusion attention rather than directly combining embeddings (ablation) | DBLM · SZ-TSSA | HR@50: 0.588$\pm$0.211 -> 0.662$\pm$0.182 | Helped |
| Add the masking mechanism (ablation) | DBLM · MCM-TSSA | HR@50: 0.426$\pm$0.359 -> 0.487$\pm$0.356 | Helped |
| Add the masking mechanism (ablation) | DBLM · SZ-TSSA | HR@50: 0.539$\pm$0.331 -> 0.662$\pm$0.182 | Helped |
Surprising findings
- Decision-making baselines like Markowitz and Fuzzy-AHP sometimes underperform simple machine learning baselines such as ECM, and several ML baselines show high variance.
Limitations
- Relies on handcrafted feature set and a fixed cosine-similarity graph threshold (0.3).
- Requires full-rank calibrations (sigmoid and epsilon regularization) that are heuristic rather than principled.
- Evaluated only on two supply chain datasets, with no public release of the data stated.
Experimental setup
Datasets: MCM SZ
Benchmarks: MCM-TSSA SZ-TSSA
Metrics: HR@10 HR@20 HR@50 MRE
Baselines: HA MC Greedy DP Fuzzy-AHP Fuzzy-TOPSIS Markowitz DT Lasso MLP ECM SGOMSM
Builds on: Black-Litterman model Markowitz mean-variance optimization ChebGCN temporal convolutional network
Closest papers by meaning
- Learning Production Functions for Supply Chains with Graph Neural Networks (AAAI 2025 · similarity 0.82)
- Latent Variable Estimation in Bayesian Black-Litterman Models (ICML 2025 · similarity 0.82)
- CI-STHPAN: Pre-trained Attention Network for Stock Selection with Channel-Independent Spatio-Temporal Hypergraph (AAAI 2024 · similarity 0.82)
- A Set-Sequence Model for Time Series (NeurIPS 2026 · similarity 0.81)
- Online Allocation with Unknown Shared Supply (NeurIPS 2026 · similarity 0.80)
- Market-GAN: Adding Control to Financial Market Data Generation with Semantic Context (AAAI 2024 · similarity 0.80)
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