多產品動態定價需求參數估計之實務流程

Abstract

因為顧客對於價格敏感，所以動態定價可以在有限的庫存與產能下，透過定價控制需求進而增加收入。然而瞭解價格如何影響需求並不是一個容易的問題，而多產品之間的替代效應使得估計需求變得更困難。雖然目前有很多研究提出各種估計模型來探討多產品間價格與需求的關係，但卻很少研究示範如何實際應用這些模型，並探討這些模型在真實問題中的預測成效。因此我們的研究提出了一個詳細的過程，來示範如何將理論的需求估計模型應用於真實的多產品定價問題，並且我們分別訓練訓練了考慮與未考慮替代效應的需求模型，以比較考慮替代效應對於需求估計的影響。對於前者，我們使用線性回歸（linear regression）和指數回歸（exponential regression），分別對每個產品做需求估計。對於後者，我們使用多項式邏輯模型（multinomial logit model）來估計產品間的選擇機率。除此之外，為了提高需求模型的估計成效，我們使用不同的產品特徵以及不同的預測器來訓練模型。我們使用一個線上鞋子零售商的銷售數據來示範需求估計的方法與流程。在此需求估計的問題中，我們發現多項式邏輯模型比線性回歸和指數回歸的結果更好，並且使用隨機森林做為預測器訓練多項式邏輯模型，比最小平方法訓練的多項式邏輯模型提高了 15% 的成果。

Because demand is price sensitive, dynamic pricing could increase revenues under limited inventory or capacity. However, how prices would affect demand quantity is a tough problem. Moreover, the substitution effect among products makes demand estimation even more complicated. Although many models have been proposed to discuss the relationship between prices and demand for multiple products, few studies have explored how to apply those models in practice and the effectiveness of those models. To bridge the gap between theory and practice, we propose a detailed process to demonstrate how to apply the demand estimation models for the multi-product pricing problem. To show the effectiveness of taking substitution effect into consideration in the models, we compare the performance of demand models with and without the substitution effect. For the models without substitution effect, we adopt linear regression and exponential regression and get the multi-product pricing policy by combining the best pricing policy for every single product. For the models with the substitution effect, we use the multinomial logit model (MNL) to estimate the choice probabilities among products. To improve our demand models' performance, we use more product features and alternative predictors to train models. An online retailing dataset is used to show our process of demand estimation. In this case, the MNL model has better performance than the regression models. Moreover, compared with the basic MNL model, which is trained with least squares regression, the MNL model with random forest improves the performance by 15%.