考虑不确定协变量下的在线广告鲁棒分配策略

doi:10.16381/j.cnki.issn1003-207x.2022.1769

Abstract

Abstract:

An online advertising contract inventory allocation model is proposed， in which covariate information is incorporated and the impression supply of targeted viewers is treated as uncertain. Owing to the fact that the joint probability distribution of viewer impression supply and covariate information is difficult to be precisely known， the model is constructed by means of a distributionally robust optimization approach. Building upon existing research， an ambiguity set based on covariate information is first formulated； subsequently， an exact algorithm is derived through the utilization of dual cone techniques. The validity of the proposed model is ultimately demonstrated via simulation experiments. Furthermore， managerial implications are provided.

Key words: online advertising, distributionally robust optimization, covariate information, guaranteed contract

CLC Number:

O221.7

Wenqiang Dai, Danyang Li. Robust Guaranteed Delivery and Allocation Optimization for Online Display Advertising with Covariate-based Information[J]. Chinese Journal of Management Science, 2025, 33(8): 230-237.

Figures/Tables 9

参数	取值
$l = 1$ 时曝光供应量的均值( $μ i 1$ )	$U (700,800)$
$l = 2$ 时曝光供应量的均值( $μ i 2$ )	$U (800,900)$
$l = 3$ 曝光供应量的均值( $μ i 3$ )	$U (900,1000)$
曝光供应量的方差( $σ i l 2$ )	$0.1 μ i l$
曝光供应量的上界( $s ¯ i l$ )	$1.3 μ i l$
广告合约 $j$ 的权重( $w j$ )	0.3
广告合约 $j$ 的连接密度 $p j$	$U (0.1,0.4)$
目标群体 $i$ 的连接密度 $p i$	$U (0.5,1)$
机会约束风险水平( $ε$ )	0.01
情景数量( $L$ )	3
每个情景出现的概率( $p l$ )	{0.7,0.1,0.2}
广告合约 $j$ 的需求量( $d j$ )	$0.2 ∑ l ∈ L ∑ i ∈ Γ (j) μ i l 3$

目标群体数 $I$	广告合约数 $J$	服务水平 (%)	非公平水平( $× 10 - 6$ )	求解时间（s）
3	20	100	1.018	2.52
	21	100	3.018	2.84
	22	100	1.541	3.39
	23	100	3.893	3.96
	24	100	7.443	3.54
	25	87.87	1.021	4.15
4	20	100	0.013	3.41
	21	100	0.166	4.14
	22	99.4	2.675	4.25
	23	100	3.124	4.27
	24	99.95	1.314	4.52
	25	100	1.413	4.92
5	20	100	0.643	3.78
	21	100	0.606	4.83
	22	86.02	0.764	5.11
	23	80.66	0.781	5.47
	24	80.00	3.978	5.48
	25	84.35	2.990	6.14
6	20	83.30	0.522	5.78
	21	94.53	0.970	5.81
	22	97.2	1.886	6.00
	23	93.25	0.591	6.12
	24	87.9	2.311	6.43
	25	83.30	0.654	6.87

$I × J$	服务水平( $%$ )		非公平水平( $× 10 - 6$ )
$I × J$	$Q S P$	$C - Q S P$	$Q S P$	$C - Q S P$
3 $×$ 20	100	100	2.880	1.018
3 $×$ 21	100	100	4.776	3.018
3 $×$ 22	91.79	100	4.081	1.541
3 $×$ 23	88.96	100	6.247	3.893
3 $×$ 24	92.37	100	7.395	7.443
3 $×$ 25	85.45	87.87	7.018	1.021

连接概率	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
服务水平( $%$ )	79.23	100	68.87	66.67	-	-	-	-	-	-
非公平水平( $× 10 - 6$ )	1.17	2.19	4.72	8.01	-	-	-	-	-	-

倍数	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
服务水平( $%$ )	100	100	99.96	80.67	-	-	-	-	-	-
非公平水平( $× 10 - 6$ )	0.607	1.34	2.96	2.37	-	-	-	-	-	-

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Robust Guaranteed Delivery and Allocation Optimization for Online Display Advertising with Covariate-based Information

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