子序列導向之多元時序資料分群與建模分析—以汽車零組件需求預測為例

Abstract

在全球供應鏈益發複雜且需求型態瞬息多變的情況下，企業若要維持適當庫存與服務品質，必須依賴高效且高精度的需求預測，尤其當產品上市時間不同、需求呈間歇波動，並伴隨替代或互補效應時更是如此。然而，逐品項獨立建模不僅計算成本高昂，也往往忽略不同序列間的互動資訊。 為因應此挑戰，本研究提出一套「先分群、後建模」的整合性預測框架。首先對齊多條需求序列的起始點，再以交叉相關係數量化其同步與領先／滯後關係，進而透過階層式演算法將具相似需求輪廓或正負相關性的序列歸為群集。分群完成後，本框架採行雙路徑預測：一路徑將群內高度相似的子序列串接為長序列並套用單變量模型，另一路徑則將整群序列同時輸入多變量模型以捕捉交互作用。針對平均絕對百分比誤差（MAPE）在低量級與零需求場景易失真的問題，本文進一步提出以實際值與預測值總和為分母的 N_MAPE 指標，使衡量結果對不同量級與間歇需求更具公平性與解釋力。 實驗以某汽車零組件之月度需求資料為例，聚焦兩種分群方式下的四個大型群集。結果顯示，在需求輪廓同向群集內，群集單變量模型可明顯改善高誤差序列，但整體平均誤差仍略遜於獨立建模；多變量模型僅於部分序列表現優於基準，群集平均 MAPE 與 N_MAPE 仍高於獨立模型，突顯跨序列交互資訊的穩定性與精度尚待提升。 整體而言，群集單變量與多變量方法唯有在序列互動關係明確且結構穩定時方能超越逐品項獨立建模，若群集雜訊過高或關聯性鬆散，無差別共享反而稀釋序列特徵。有效的策略是在基準誤差偏高且具高度關聯性的子集合中導入共用模型，藉由精細的群內篩選與差異化建模路徑，將跨序列資訊轉化為可觀的預測增益。此策略性分群與建模原則凸顯了本研究於特定序列顯著提升預測效能的價值，並為未來跨產業導入共享預測模型提供可行的實務指引。

Accurate and efficient demand forecasting is essential in today’s complex supply chains, where demand is often intermittent, product life cycles are misaligned, and substitution or complementarity effects exist. Traditional item-level models are computationally costly and often neglect cross-series relationships. To address this, we propose a “cluster-first, model-second” forecasting framework that first aligns the starting points of multiple time series, then applies cross-correlation to quantify lead–lag relationships, followed by hierarchical clustering based on profile similarity or positive/negative correlations. The framework supports two parallel modeling paths: a univariate path that concatenates similar subsequences for individual modeling, and a multivariate path that inputs entire clusters into VARMA and LSTM models to capture interdependencies. To address the distortion of MAPE under low or zero demand, we introduce N_MAPE, which normalizes error by the sum of actual and predicted values. Using monthly automotive parts demand data, we evaluate four large clusters derived from two grouping strategies. Results show that clustered univariate models improve high-error series but underperform in average accuracy compared to independent models. Multivariate models yield limited gains and higher average errors, highlighting sensitivity to noise and structural inconsistency. Overall, the framework is most effective when applied to highly correlated, high-error subsets. Indiscriminate shared modeling may dilute useful signals, while strategic clustering and selective model deployment can meaningfully enhance forecasting performance across industries.