基于XGBoost算法的数据驱动单周期报童问题研究

doi:10.16381/j.cnki.issn1003-207x.2020.0816

Abstract

Abstract:

Solving single-period newsvendor problem usually assumes that the demand distribution follows a particular form， predicts demand from historical data， then solves optimization models. Although this assumption simplifies the analysis， it does not reflect the true distribution of demand over time and inevitably passes on historical estimated prediction errors to the optimization process. To solve this problem， a method that combines estimation and optimization is proposed. This method adopts the form of data-driven weights to deal with the demand uncertainty related to features and introduces XGBoost algorithm to solve single- period newsvendor problem with non-stationary demand. After observing the features that affect demand， the method directly determines the optimal inventory decision. This paper's contribution to the field of operations management mainly includes twofold： 1） It integrates a scalable end-to-end tree boosting system called XGBoost into a single-period newsvendor problem. 2） The integrated estimation optimization algorithm is applied to a real-world data set under different target service levels and training sample sizes， and is compared with several standard methods for studying newsvendor problems. The results show that this method can reduce inventory costs by at least about 5%.

Key words: newsvendor, machine learning, sample average approximation, quantile regression, optimization

CLC Number:

F274

Yuting Yan,Wenjie Bi. A Data-driven Single-Period Newsvendor Problem Based on XGBoost Algorithm[J]. Chinese Journal of Management Science, 2024, 32(1): 260-267.

Figures/Tables 7

方法	cost	?cost	SL	参数
XO- $l 1$	47814.28	59.82%	0.61	5
XO- $l 2$	46588.57	60.85%	0.6	5
XGBoost点预测	51887.34	56.39%	0.58	—
线性回归点预测	66671.92	43.97%	0.49	—
Lasso点预测	65668.30	44.81%	0.52	0.1
岭回归点预测	66619.21	44.01%	0.49	1
SAA	118988.57	—	0.43	—

方法	TSL=0.6			TSL=0.7			TSL=0.8
方法	cost	?cost（%）	SL	cost	?cost（%）	SL	cost	?cost（%）	SL
XO-- $l 1$	55868.57	59.75	0.59	47814.28	59.82	0.61	41901.43	59.75	0.8
XO-- $l 2$	57486.67	58.59	0.49	46588.57	60.85	0.6	43802.5	57.93	0.78
XGBoost点预测	63106.33	54.54	0.51	51887.34	56.39	0.58	46942.5	54.91	0.62
线性回归点预测	77783.91	43.97	0.43	66671.92	43.97	0.49	58337.93	43.97	0.49
Lasso点预测	76613.02	44.81	0.49	65668.30	44.81	0.52	57459.76	44.81	0.52
岭回归点预测	77722.42	44.01	0.52	66619.21	44.01	0.49	58291.81	44.01	0.49
SAA	138820.0	—	0.49	118988.57	—	0.43	104115.0	—	0.43

方法	S= 0.2			S= 0.4			S= 0.6			S= 0.8			S= 1.0
方法	cost	?cost（%）	SL	cost	?cost（%）	SL	cost	?cost（%）	SL	cost	?cost（%）	SL	cost	?cost（%）	SL
XO- $l 1$	52202.85	56.13	0.65	47317.14	60.23	0.62	50630.98	57.45	0.59	48431.42	59.30	0.62	47814.28	59.82	0.61
XO- $l 2$	54591.42	54.12	0.7	48054.28	59.61	0.71	49485.71	58.41	0.59	49151.42	58.69	0.55	46588.57	60.85	0.6
XGBoost点预测	57887.34	51.35	0.56	54329.75	54.34	0.55	52265.71	56.08	0.56	52416.32	55.95	0.56	51887.34	56.39	0.58
线性回归点预测	72756.51	38.85	0.48	69844.55	41.30	0.47	66535.08	44.08	0.48	66538.08	44.08	0.48	66671.92	43.97	0.49
Lasso点预测	71071.79	40.27	0.54	65607.61	44.86	0.5	63785.62	46.39	0.57	64751.26	45.58	0.5	65668.30	44.81	0.52
岭回归点预测	72252.52	39.28	0.48	68930.05	42.07	0.47	66381.74	44.21	0.49	66417.88	44.18	0.48	66619.21	44.01	0.49
SAA	118988.6	—	0.43	118989	—	0.43	118988.7	—	0.43	118988.57	—	0.43	118988.57	—	0.43

参数	含义	样本量
参数	含义	0.2	0.4	0.6	0.8	1
learning_rate	每步迭代步长	0.01	0.01	0.13	0.11	0.1
n_estimators	控制弱学习器数目，即最大迭代次数	500	500	500	500	500
max_depth	树的最大深度，用来控制过拟合	7	9	7	6	9
min_child_weight	子集的所有观察值的最小权重和，控制过拟合	9	9	5	3	9
subsample	构建每棵树样本采样率，用于训练模型子样本占整个样本集合的比例	0.8	0.7	0.8	0.8	0.8
colsample_bytree	列采样率，即特征采样率	0.8	0.8	0.8	0.8	0.8
gamma	分裂节点时损失函数减小值只有大于gamma节点才分裂，值越大算法越不容易过拟合	0.3	0	0	0	0.3
权重 $l 1$ 正则项	$l 1$ 正则项的参数，用来防止过拟合	1	10	5	10	5
权重 $l 2$ 正则项	$l 2$ 正则项的参数，用来防止过拟合	0	5	10	20	5

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数据类别	特征
产品	产品id、重量、件数、品牌, 品牌名
商店	商店id、商店名, 商店类型
地理位置	商店id、州、城镇
交易数据	周数、商店id、产品id、销量、销售渠道、销售路线、销量滞后值、销量均值滞后值（按商店、产品和品牌不同指标分类）
时间	周数、产品上次销售时间, 产品首次销售时间（按时间和产品分类）

方法	RMSE	MAE	中位数绝对误差	R2
XGBoost点预测	46.91	25.58	10.18	0.8
线性回归点预测	53.19	35.30	24.18	0.74
Lasso点预测	52.79	34.77	24.28	0.75
岭回归点预测	53.16	35.27	24.18	0.75

A Data-driven Single-Period Newsvendor Problem Based on XGBoost Algorithm

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