(681b) Graph Neural Networks for Supply Chain Inventory Management

Major disruptions since the COVID-19 pandemic have forced companies to rethink inventory management policies. Making decisions at one time period requires information about future customer demand, and often, information is not shared among different echelons, leading to suboptimal inventory management policies. Supply chain inventory management is not a new field. Many different methods have been explored in the supply chain inventory management space, from deterministic and stochastic mathematical programming models [1] to recent reinforcement learning techniques [2]. Given the graph structural nature of supply chain networks, with this research, we seek to understand how we can leverage graph neural networks to improve supply chain inventory management.

Instead of tabular inputs to neural networks, graph neural networks (GNN) take in graphical inputs with a set of features associated with each node. GNNs can be used to make predictions on different levels, whether that is node-level, graph-level, or even missing link predictions. One of the known properties of graph neural networks is their ability to generalize to different structures [3, 4]. Deterministic mathematical programming models provide optimal solutions but can be computationally expensive, especially once the size of the problem increases. Given the capability of generalization of graph neural networks, we show that these networks can generalize to other unknown structures.

As a proof-of-concept problem, we consider a serial single-product supply chain network as reported in the paper by Hubbs et al. [5]. Data is generated for different structures using a deterministic mixed-integer linear program (MILP) with stochastic demand realizations. This model finds the optimal reorder quantity for each network node that maximizes the entire system's net revenue. A GNN is trained on this data and used to make predictions on the optimal reorder quantities for each node within the network. We connect this model with a simulation environment, which enforces feasibility.

We develop a custom message-passing neural network (MPNN) architecture that provides better predictions than off-the-shelf graph neural network software. The MPNN involves a concatenation step of neighboring features per node followed by a Multi-Layer Perceptron (MLP). We show that the MPNN performs very well for in-distribution networks and provides close to optimal reorder predictions during non-startup and shut-down periods. For in-distribution samples, the MPNN connected with the environment provides close to optimal results with less than a 1% optimality gap for in-distribution networks and around a 1-5% optimality gap for out-of-distribution networks.

References

[1] D. Simchi-Levi and Y. Zhao, “Performance evaluation of stochastic multi-echelon inventory systems: A survey,” Advances in Operations Research, vol. 2012, pp. 1–34, 2012. doi:10.1155/2012/126254

[2] B. Rolf et al., “A review on reinforcement learning algorithms and applications in supply chain management,” International Journal of Production Research, vol. 61, no. 20, pp. 7151–7179, Nov. 2022. doi:10.1080/00207543.2022.2140221

[3] S. Qin, R. Van Lehn, V. Zavala, and T. Jin, Predicting critical micelle concentrations for surfactants using graph convolutional neural networks, Apr. 2021. doi:10.26434/chemrxiv.14384693.v1

[4] K. D. Lamb and P. Gentine, “Zero-shot learning of aerosol optical properties with graph neural networks,” Scientific Reports, vol. 13, no. 1, Oct. 2023. doi:10.1038/s41598-023-45235-8

[5] C. D. Hubbs et al., “OR-gym: A reinforcement learning library for operations research problems,” 8 2020