Demand Forecasting: Temporal Graph Networks for Retail

The business problem

Retailers lose $1.1 trillion globally to inventory distortion: $634 billion from out-of-stocks and $472 billion from overstocks. Accurate demand forecasting is the single highest-leverage optimization in retail operations. Even a 1% improvement in forecast accuracy reduces inventory costs by 5-10%.

Traditional forecasting models (ARIMA, Prophet, LSTM) treat each product-store combination as an independent time series. They miss the dependencies: a Coca-Cola promotion cannibalizes Pepsi demand. A snowstorm in Chicago affects salt demand in Milwaukee. A viral TikTok video creates sudden correlated demand across geographies. These cross-product and cross-store effects are graph-structured.

Why flat ML fails

• Independent forecasts: Time series models forecast each SKU-store separately. They cannot model substitution effects (Coke promo reduces Pepsi demand) or complementary effects (chips drive salsa sales).
• No spatial correlation: Stores 5 miles apart serve overlapping customers. Weather, events, and demographics create correlated demand patterns that independent models ignore.
• Promotion blindness: A promotion on one product affects demand for related products. Flat models need hand-engineered cross-product features that are brittle and incomplete.
• New product cold start: New products with no history get no forecast. Graph-based models can transfer patterns from similar products.

The relational schema

Node types:
  Product  (id, category, brand, price, shelf_life)
  Store    (id, format, sqft, geo_lat, geo_lon)
  Promo    (id, type, discount_pct, start_date, end_date)

Edge types:
  Product --[substitute_of]--> Product  (elasticity)
  Product --[complement_of]--> Product  (lift_factor)
  Store   --[near]-->          Store    (distance_km)
  Promo   --[applies_to]-->   Product
  Product --[sold_at]-->       Store    (daily_units, date)

PyG architecture: SAGEConv + temporal regression

We use SAGEConv for spatial aggregation (cross-product, cross-store) combined with a GRU cell for temporal dynamics. Each product-store node gets a time-varying embedding that captures both its own history and its neighbors' influence.

import torch
import torch.nn.functional as F
from torch_geometric.nn import SAGEConv, Linear

class DemandGNN(torch.nn.Module):
    def __init__(self, node_dim, hidden_dim=128, seq_len=28):
        super().__init__()
        self.node_lin = Linear(node_dim, hidden_dim)

        # Spatial: aggregate from substitutes, complements, nearby stores
        self.conv1 = SAGEConv(hidden_dim, hidden_dim)
        self.conv2 = SAGEConv(hidden_dim, hidden_dim)

        # Temporal: GRU over daily snapshots
        self.gru = torch.nn.GRU(
            input_size=hidden_dim, hidden_size=hidden_dim, batch_first=True)

        # Regression head: predict next 7 days of demand
        self.head = torch.nn.Sequential(
            Linear(hidden_dim, 64),
            torch.nn.ReLU(),
            Linear(64, 7),  # 7-day forecast horizon
        )

    def forward(self, x_seq, edge_index):
        # x_seq: (num_nodes, seq_len, node_dim)
        B, T, D = x_seq.shape
        embeddings = []

        for t in range(T):
            x = self.node_lin(x_seq[:, t, :])
            x = F.relu(self.conv1(x, edge_index))
            x = self.conv2(x, edge_index)
            embeddings.append(x)

        # Stack temporal embeddings and run GRU
        h_seq = torch.stack(embeddings, dim=1)  # (B, T, H)
        _, h_final = self.gru(h_seq)

        # Predict next 7 days
        return self.head(h_final.squeeze(0))  # (B, 7)

Training considerations

• Loss function: Use quantile regression loss to produce prediction intervals (P10, P50, P90), not just point estimates. Inventory planning needs uncertainty bounds.
• Temporal split: Train on 12 months of history, validate on month 13, test on month 14. Shift the window weekly for rolling evaluation.
• Graph construction: Substitute/complement edges can come from purchase basket analysis or category taxonomy. Store-proximity edges use geographic distance thresholds.
• Feature encoding: Calendar features (holiday, day-of-week), promotion flags, weather, and recent sales velocity are critical temporal node features.

Expected performance

Demand forecasting is a regression task. The right metric is Weighted Mean Absolute Percentage Error (WMAPE), not AUROC:

• ARIMA (per-SKU): ~18% WMAPE
• LightGBM (flat-table): ~14% WMAPE
• GNN (SAGEConv + GRU): ~10-12% WMAPE
• KumoRFM (zero-shot): ~10% WMAPE

Or use KumoRFM in one line

PREDICT daily_units FOR product, store
USING product, store, promotion, sales_history

KumoRFM replaces the graph construction, temporal architecture, and training pipeline with a single query. It handles substitute/complement discovery, seasonal patterns, and promotion effects automatically, matching or exceeding hand-tuned GNN forecasters.