台灣美髮美容產業市場高度分散、以中小型店家為主，普遍面臨顧客留存不易、新客獲取成本偏高的經營挑戰。現行客戶關係管理（Customer Relationship Management， CRM）系統多採固定週期的規則式提醒，缺乏對個別顧客回訪時機的預測能力，導致店家常在不恰當的時間點聯繫顧客而錯失回訪。本研究針對美髮業顧客回訪時間預測問題，僅利用既有銷售點（point-of-sale， POS）系統累積的歷史交易資料，提出一個以業務成效為導向的異質圖神經網路 regression 架構。該架構以跨店全局異質圖（8 種節點、多種邊類型）建模顧客－設計師－服務之間的異質關係，串接三層 Heterogeneous GAT encoder、temporal encoding、cross-split causal history Transformer 與 raw feature bypass，並注入最佳 baseline 梯度提升樹方法（Gradient Boosting Machine， GBM）的預測作為殘差特徵（GBM-residual stacking），最後以結合 days-space Huber、direct-days、15 天 hinge 與 bucket 輔助的組合式損失（multi-loss）訓練，並以業務指標導向的 composite metric-aware early stopping 選模。 在與本研究完全相同的 89 維輸入與同一測試集（n = 103，382）下，本研究模型達到平均絕對誤差（Mean Absolute Error， MAE）8.5650 天、均方根誤差（Root Mean Squared Error， RMSE）13.1118 天、15 天內準確率 79.50%，相對 MAE 最低之最佳 baseline GBM（MAE 10.3951、RMSE 15.8021、15 天內準確率 74.35%）全面領先（MAE 改善 1.83 天、約 17.6%；15 天內準確率提升 5.15 個百分點）。此差距通過 Wilcoxon signed-rank、paired t-test 與 McNemar 配對檢定（皆 p < 0.001），且 95% 信賴區間 [−1.8687， −1.7906] 不含 0；於 14 個時間窗的 walk-forward 重訓重測中對 GBM 取得 12 勝 2 負，顯示跨時間切點之穩健性。本研究的主要貢獻為：在相同特徵輸入下，以異質圖結構搭配跨切割因果歷史與組合式設計，於回訪時間預測上顯著超越最佳 baseline GBM，為店家在最佳時機主動聯繫顧客提供可量化的技術基礎。此處統計顯著（p < 0.001 且 95% 信賴區間不含 0）的實務意義在於：本研究模型的領先並非來自測試集的抽樣偶然，而是可在同規模資料上穩定重現的差距，這對於將模型實際部署於 CRM 名單生成、據以安排主動聯繫時程，具有可信賴的決策價值。;The Taiwanese hair-salon and beauty industry is highly fragmented and dominated by small and medium-sized stores， which commonly struggle with customer retention and high new-customer acquisition costs. Existing customer relationship management (CRM) systems rely on fixed-cycle， rule-based reminders and cannot predict when an individual customer will return， so stores often contact customers at the wrong time and lose repeat visits. This study addresses customer return-time prediction for the hair-salon industry using only the historical transaction records already accumulated in the point-of-sale (POS) system， and proposes a business-oriented heterogeneous graph neural network regression architecture. The architecture builds a single cross-store global heterogeneous graph (8 node types and multiple edge types) to model the heterogeneous relations among customers， designers and services， and combines a three-layer Heterogeneous GAT encoder， temporal encoding， a cross-split causal history Transformer and a raw feature bypass; it further injects the prediction of the best baseline， GBM， as a residual feature (GBM-residual stacking)， is trained with a multi-loss objective (a days-space Huber loss， a direct-days loss， a 15-day hinge loss and a bucket auxiliary loss)， and is selected with a business-oriented composite metric-aware early-stopping criterion. Under exactly the same 89-dimensional input and the same test set (n = 103，382)， the proposed model achieves an MAE of 8.5650 days， an RMSE of 13.1118 days and a 15-day accuracy of 79.50%， outperforming the lowest-MAE best baseline GBM (MAE 10.3951， RMSE 15.8021， 15-day accuracy 74.35%) on all three metrics (MAE improved by 1.83 days， about 17.6%; 15-day accuracy improved by 5.15 percentage points). The gap is statistically significant under paired Wilcoxon signed-rank， paired t-test and McNemar tests (all p < 0.001)， with a 95% confidence interval of [−1.8687， −1.7906] that excludes zero; in a 14-window walk-forward retrain-and-retest protocol the proposed model beats GBM 12 to 2， demonstrating robustness across temporal splits. The main contribution is that， under identical feature input， combining a heterogeneous graph structure with cross-split causal history and a composite design significantly surpasses the best baseline GBM on return-time prediction， providing a quantifiable technical basis for stores to proactively contact customers at the right time.
