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.
Gerçek Budak, Faraz Gholamzadeh Gharehgheshlaghi, Melika Barjesteh Vaezi +1cs.AI
The coffee supply chain is one of the most complex agri-food networks, marked by geographically dispersed production, multi-tier coordination, and high sensitivity to quality and freshness. While sustainability and digitalization have gained attention, demand forecasting, optimization, and traceability are often treated separately. This study presents a two-phase integrated framework. First, a hybrid CNN-LSTM model is used for demand forecasting. On the public Coffee Chain Sales dataset with chronological 70/15/15 splitting, the model achieves MAE of 22.87 and R^2 of 0.90, outperforming the best deep learning benchmark by ~12% and classical methods by over 30%. In the second phase, the forecasted demand feeds a tri-objective mixed-integer linear programming (MILP) model that jointly minimizes cost, minimizes carbon emissions, and maximizes product freshness in a multi-period, multimodal, closed-loop supply chain with circular recovery. Freshness is modeled via exponential decay based on inventory age. Using the epsilon-constraint method, 25 Pareto solutions are obtained. Sensitivity and policy analyses show that balanced sustainability policies can reduce emissions by 22.4% with only a 9.9% cost increase while maintaining near-optimal freshness. Keywords: Coffee supply chain; Deep learning; Demand forecasting; Multi-objective optimization; Circular economy; CNN-LSTM; Mixed-integer linear programming.