Spatiotemporal Prediction of Medical Device Sales Using Hybrid LSTM GNN in South Sumatra

Abstract

Forecasting medical device purchases at the regional level supports equitable allocation, procurement planning, and distribution scheduling across administrative regions. In developing regions where infrastructure and logistics capacity are unevenly distributed, anticipating regional purchase patterns mitigates supply imbalances and improves the continuity of clinical services. The demand for medical devices exhibits complex spatiotemporal characteristics, where demand variations are influenced by temporal dynamics and interregional spatial connectivity. The objective of this study is to apply and evaluate a Hybrid Long Short-Term Memory and Graph Neural Network (LSTM-GNN) model for predicting the spatiotemporal demand for medical devices, to analyze the effect of spatial relationships on demand variations, and to identify optimal hyperparameter combinations. The methodology uses medical device sales data from PT Parit Panjang, a distribution company in South Sumatra, covering July 2020 to October 2025, comprising 10,878 unique invoices across 16 regencies and cities (Musi Rawas Utara, with only 2 invoices in the study period, was merged into Musi Rawas). Records were aggregated into a daily panel, split chronologically into training, validation, and testing sets (July 2020 to December 2023, January to December 2024, and January to October 2025), and normalized with a log transformation fitted on the training set only. Because 81.54% of all daily region-level targets across the full panel are zero (84.85% in the test period), the problem is formulated as zero-inflated forecasting with two stages: a binary classifier that predicts whether a sale occurs and a regression model that predicts the sales amount on non-zero days. A binary COVID-19 pandemic indicator (July 2020 to December 2022) is included as an exogenous input channel. A spatial graph was built from regional proximity using Haversine distance with three nearest neighbors and a maximum distance threshold of 104.66 km. Temporal dynamics were modeled with LSTM, spatial dependencies with a Graph Convolutional Network (GCN), and both representations were combined through concatenation followed by a fully connected layer. The Hybrid LSTM-GNN achieved an R-squared of 0.0523, an RMSE of 8,002,603 IDR, and a MAE of 1,881,358 IDR on the original scale, outperforming the standalone LSTM (R-squared 0.0433), the standalone GNN (0.0059), and the always-zero baseline (0.0059). The classification stage achieved 90.67% accuracy and an AUC of 0.861. Diebold-Mariano tests confirm that the hybrid model improves over the standalone LSTM and GNN and over the statistical baselines at p < 0.001, but its practical advantage is limited to the classification stage. A random search over 30 configurations identified a superior configuration (LSTM hidden 219, GNN hidden 107, dropout 0.17) reaching an R-squared of 0.0582, the best among all evaluated models. The COVID-19 indicator provides a small improvement, and replacing the distance-based graph with the actual distribution network (a star centered on Palembang) raises the R-squared to 0.0703. In conclusion, the zero-inflated Hybrid LSTM-GNN framework supports regional medical device sales forecasting and distribution planning, with the classification stage providing the dominant predictive signal.