以增強 Lotka–Volterra model預測具競爭關係的零售模式

Abstract

本篇論文開發一種新的預測方法，可以用來分析及預測兩種零售模式的競爭關係，進行這種預測的傳統預測方法是基於Lotka-Volterra model（以下簡稱LV模型）。 LV模型假設每個物種的族群數量受到自身生長，物種內部交互作用及其他物種的外部交互作用所影響。大多數商業應用研究直接使用銷售數據輸入LV模型。當銷售數據受到季節性變化影響的時候，先前的方法可能會導致錯誤的結論，因為原始的LV模型的並未考慮到季節性變化的影響。因此，本篇論文提出了一個預測方法（LV模型的增強應用）。每個零售模式的銷售數據被視為複合數據，並將複合數據分解為三個單獨的部分：（1）總計（2）競爭和（3）季節成分。LV模型用於預測競爭關係；其他兩個組件由典型的時間序列方法預測；並將三個部分數據最終組合成一個。實證研究表明，新的預測方法在預測預測誤差方面，基本上優於傳統預測方法（新方法便利導向預測誤差為4.4％、傳統預測方法為16.7％；新方法預算導向預測誤差為5.8％、傳統預測方法為16.2％）。 此外，新的預測方法所揭示的競爭模式是更有說服力的捕食者 -獵物關係，其結論是便利導向的零售模式是捕食者。相反地，傳統預測方法的結論是預算導向的零售模式是捕食者，是相當令人懷疑的，因為隨著時間的推移，便利導向的零售模式將隨著GDP的增長相較於預算導向的零售模式會有較快的成長。本篇論文為如何適當應用LV模型預測銷售數據和分析兩種商業模式的競爭關係做出了貢獻。 關鍵詞：Lotka–Volterra 模型，預測，零售模式

his research develops a sales forecasting model that can analyze the interaction effects of two retail competing formats (Convenience-oriented vs. Budget-oriented formats). A traditional approach to making such a forecast is based on the Lotka–Volterra equations (also called the LV-model). The LV-model assumes that the population of each species is affected by its self-growth, internal interaction within the species, and external interaction with other species. Most prior studies in business applications directly use sales data as input to the LV-model. The prior approach may result in misleading conclusions when sales data are embedded with seasonal variation, because this variation is not addressed in the original development of the LV-model. Therefore, this study proposes a forecasting framework (an enhanced application of the LV-model). The sales data of each retail format is considered as a compound data, which is decomposed into three individual components: (1) aggregate, (2) competition, and (3) seasonal components. The LV-model is used to forecast the competition component；the other two components are forecasted by typical time series methods；and the data of three components are finally combined into one. Empirical study indicates that the proposed method substantially outperforms the prior approach in terms of forecasting errors (4.4% vs.16.7% for Convenience-oriented and 5.8% vs. 16.2% for Budget-oriented). In addition, the proposed method reveals a more convincing predator-prey relationship between the two retail formats, which concludes that the Convenience-oriented is the predator. To the opposite, the prior approach, concluding that the Budget-oriented is the predator, is quite doubtful because the Convenience-oriented shall be preferred while the GDP grows over time. This research makes a contribution in how to appropriately apply the LV-model in forecasting revenue and analyzing the interaction effects of two competing business species. Keywords : Lotka–Volterra model ; Forecasting ; Retail formats