We study the strategic design of a two-echelon spare-parts inventory network where evaluating each candidate topology requires an expensive inventory optimization model. The design partitions hundreds of sites into feasible clusters and selects a central replenishment site for each cluster to reduce costs while maintaining service levels. Because the optimizer favors candidates with high predicted savings, it can exploit optimistic surrogate errors. We develop a conservative framework combining a graph neural network ensemble, variable neighborhood search, and set-partitioning recombination. The surrogate is trained on exact cluster evaluations, while a lower quantile of ensemble-predicted savings guides the search to limit optimism. Clusters found during the search are recombined through set partitioning using surrogate-based objective coefficients. The resulting network is evaluated with the exact inventory model, and only this evaluation is used to report performance. In a case study of 246 fulfillment centers in Amazon's North American network, the framework improves combined savings by 30.5% over an optimization baseline based entirely on exact cluster evaluations, while maintaining approximately 99.8% service across six independent replications. Under equal computational budgets, graph-surrogate-guided search achieves higher mean exact savings than a tabular alternative under both scoring schemes. Conservative scoring improves mean savings for both surrogate classes and reduces the share of final-network clusters overestimated by the graph surrogate from 68% to 28%. Predictive and ranking accuracy deteriorate among search-generated candidates with high surrogate scores, indicating that random holdout performance can incompletely characterize surrogate quality during optimization.
Inventory and distribution planning in Physical Internet networks requires coordinating factory-hub assignments, factory supply, lateral transshipment among collaborative hubs, retailer deliveries, and shortages. The problem combines discrete assignment decisions with interdependent continuous flows, while uncertain operating costs make robust planning more difficult. This study formulates deterministic and min-max regret models for a three-echelon network of factories, hubs, and retailers and develops a graph neural network-guided genetic algorithm (GNN-GA) for the assignment decisions. The GNN estimates hub-specific factory-selection probabilities that are used to construct the initial GA population and adapt mutation according to prediction uncertainty. Each previously unseen candidate assignment is evaluated by solving the remaining continuous-flow problem to LP optimality. Simulated annealing, a standard GA, and GNN-GA are compared on 15 instances using matched random seeds and fixed limits on distinct assignment evaluations. Because the evaluation budgets for test Instances 13-15 are smaller than the nominal population size, these experiments primarily assess the quality of learned initialization rather than multi-generation evolutionary search. A separate 400-evaluation experiment on exact test Instance 13 permits three complete offspring generations and a partial fourth pass, with GNN-GA outperforming GA in all 10 matched runs. Three independently generated exact-solvable instances provide a separate test of transfer. Ablation results show that learned initialization provides most of the improvement, while entropy-guided mutation has a smaller, instance-dependent effect. Per-instance solution times include GNN inference and search but exclude model training and one-time model setup.
Graph Neural Networks (GNNs) have emerged as a powerful, differentiable class of learning models for graph-structured systems. Their ability to generalize across topologies opens the prospect of a surrogate for combined structural and parametric optimization, which classical metamodels cannot offer. Supply chains are a natural target, yet the use of GNN surrogates for supply chain problems is largely unexplored. This paper lays the foundation, presents initial steps, and discusses key research directions. As a foundation, we formulate the problem and create a large public training dataset of programmatically generated supply chain graphs with input parameters and steady-state performance metrics obtained using our SupplyNetPy simulation library. As initial steps, we explore GNN architectures that work well as surrogates for node- and network-level predictions, and analyze their accuracy-compute trade-off against simulation. Most importantly, we outline the exciting directions this opens, namely gradient-based optimization over topology, fast design-space exploration, and sensitivity analysis.
This paper introduces SupplyNetPy, an open-source, well-documented Python library for modeling and discrete-event simulation of supply chain networks with arbitrary multi-echelon structures. It supports multiple replenishment policies, perishable inventory, node disruptions, and stochastic demand and lead times. All components are extensible via inheritance. Users describe a supply chain as a graph with node and link attributes, while the library handles simulation, providing logs and extensive node and network level performance reports. This paper presents the motivation, design, key features, and architecture of SupplyNetPy, along with detailed validation results (against analytical benchmarks, a commercial tool, and a published case study). A key motivation behind SupplyNetPy's development is programmatic generation and simulation of complex models, enabling design-space exploration, what-if analysis, training data generation, and supply chain digital twins.