Time Series Supplier Allocation via Deep Black-Litterman Model

TL;DR

This work introduces the Deep Black-Litterman Model (DBLM) for Time Series Supplier Allocation by learning a data-driven perspective matrix through spatio-temporal graph neural networks and integrating it into a Black-Litterman optimization framework. It tackles lack of supervisory signals and data unreliability with a Spearman-based masked ranking loss and a masking mechanism, enabling robust future allocation predictions. Empirical results on two datasets demonstrate that DBLM consistently outperforms traditional and STGNN-based baselines, achieving substantial improvements in hit ratios at various cutoffs and reducing risk exposure. The approach provides a practical, scalable method to balance supplier profits and shortage risks in dynamic supply networks, with broad implications for resilient, data-driven supply chain decision-making.

Abstract

Time Series Supplier Allocation (TSSA) poses a complex NP-hard challenge, aimed at refining future order dispatching strategies to satisfy order demands with maximum supply efficiency fully. Traditionally derived from financial portfolio management, the Black-Litterman (BL) model offers a new perspective for the TSSA scenario by balancing expected returns against insufficient supply risks. However, its application within TSSA is constrained by the reliance on manually constructed perspective matrices and spatio-temporal market dynamics, coupled with the absence of supervisory signals and data unreliability inherent to supplier information. To solve these limitations, we introduce the pioneering Deep Black-Litterman Model (DBLM), which innovatively adapts the BL model from financial roots to supply chain context. Leveraging the Spatio-Temporal Graph Neural Networks (STGNNS), DBLM automatically generates future perspective matrices for TSSA, by integrating spatio-temporal dependency. Moreover, a novel Spearman rank correlation distinctively supervises our approach to address the lack of supervisory signals, specifically designed to navigate through the complexities of supplier risks and interactions. This is further enhanced by a masking mechanism aimed at counteracting the biases from unreliable data, thereby improving the model's precision and reliability. Extensive experimentation on two datasets unequivocally demonstrates DBLM's enhanced performance in TSSA, setting new standards for the field. Our findings and methodology are made available for community access and further development.

Figures (5)

• Figure 1: An example of TSSA problem. The building symbolizes the enterprise, and the truck represents suppliers. Green signs indicate materials, while fire denotes the risk of shortfalls. The combination of a prohibition and fire signifies no risk, and a question mark indicates unknown risks.
• Figure 2: Overall framework of DBLM. DBLM constructs the feature and propagation matrix, then extracts spatial and temporal embeddings using ChebyGCN and TCN. It fuses these embeddings to obtain $\mathcal{P}$ and $\Omega$ through ST attention. Finally, DBLM solves for $\mathcal{W}^*$ in the BL model, projecting future allocations. Masked Ranking Loss is used for DBLM supervision.
• Figure 3: The Risk Matrix (Left.) composed of the top 9 and bottom 9 suppliers sorted by ascending risk, along with their corresponding Allocation Weight Matrix (Right.) and Perspective Matrix (Middle.).
• Figure 4: (Left.) Hyper-parameter study with $\delta$ on MCM and SZ datasets from 0.01 to 1.0. (Right.) Hyper-parameter study with $\tau$ on MCM and SZ datasets from 0 to 50.
• Figure 5: Robustness study of HR@50 by randomly masking $\mathcal{O}$ and $\mathcal{S}$ in training data on MCM dataset. Mask Ratio is from 0 to 0.99.

Theorems & Definitions (7)

• definition 1: Order-Supply Mechanism Data
• definition 2: Black-Litter Model for Supplier Allocation
• definition 3: Time Series Supplier Allocation
• theorem 1
• theorem 2
• theorem 3
• lemma 1