CPC模式下保量合同的在线展示广告投放策略优化

doi:10.16381/j.cnki.issn1003-207x.2021.2559

Abstract

Abstract:

Online display advertising is developing rapidly， and the cost-per-click （CPC） contract is an important form of contract for online display advertising. Based on reality， the impression supply is usually uncertain when making advertising delivery decisions， and its probability distribution is difficult to accurately know， and only partial distribution information is known. Using the distributionally robust optimization framework， an uncertain set characterized by known information is constructed， and the optimal advertising strategy in the worst case. Then a distributionally robust chance-constrained formulation is established and a solution algorithm is given， and some numerical experiments are carried out. The results of the numerical experiments show that the designed advertising optimization model and the corresponding solution algorithm have good performance.

Key words: online display advertising, CPC, guaranteed delivery, stochastic optimization, distributionally robust

CLC Number:

O221.7

Wenqiang Dai,Weijia Chu,Jing Zhong. Online Display Advertising Optimization Based on Guaranteed Delivery Contract under CPC Model[J]. Chinese Journal of Management Science, 2024, 32(10): 256-264.

Figures/Tables 9

变量	(0.1,0.2)	(0.1,0.4)	(0.1,0.6)	(0.1,0.8)	(0.1,1)
服务水平	0.985	1	1	0.897	1
风险水平	0	0.003	0	0	0.001
运行时间( $s$ )	241.35	240.76	193.87	330.87	211.50
	(0.2,0.4)	(0.2,0.6)	(0.2,0.8)	(0.2,1)	(0.3,0.4)
服务水平	1	1	1	1	1
风险水平	0.203	0.065	0.076	0.074	0.153
运行时间( $s$ )	262.63	230.98	286.49	210.64	215.62
	(0.3,0.6)	(0.3,0.8)	(0.3,1)	(0.4,0.6)	(0.4,0.8)
服务水平	1	1	0.977	1	1
风险水平	0	0	0	0	0
运行时间( $s$ )	293.15	395.80	225.13	211.49	206.94
	(0.4,1)	(0.5,0.6)	(0.5,0.8)	(0.6,0.8)	(0.7,0.8)
服务水平	1	1	1	1	1
风险水平	0	0	0	0.023	0.021
运行时间( $s$ )	271.82	208.36	220.71	302.52	230.64

参数	平均供给 $μ i$	预算 $d j$	保证点击量 $g j$	每点击价格 $b i j$	点击率 $C T R i j$
值	[1000,2000]	[2000,4000]	[500,700]	[1,3]	[0.05,0.3]

序号	$m$	$n$	服务水平	风险水平	运行时间( $s$ )
1	3	3	1	0	89.27
2	5	3	1	0.001	160.04
3	5	5	0.998	0	182.54
4	7	5	1	0	254.53
5	7	7	0.995	0.002	665.53
6	9	7	1	0	1667.24

序号	$m$	$n$	求解方法	服务水平	风险水平	运行时间( $s$ )
1	3	3	SAA	1	0.027	60.89
1	3	3	MISOCP	1	0	89.27
2	5	5	SAA	0.994	0.032	389.51
2	5	5	MISOCP	0.998	0	182.54
3	7	7	SAA	0.989	0.018	1308.76
3	7	7	MISOCP	0.995	0.002	665.53
4	9	9	SAA	0.995	0.012	4898.20
4	9	9	MISOCP	1	0	3220.91

预算 $d 1$	1600	1800	2000	2200	2600	3000	3400
服务水平	0.944	0.992	0.998	1	0.998	0.998	1
风险水平	0.262	0.108	0.026	0	0	0	0
预算 $d 2$	1600	1800	2000	2200	2600	3000	3400
服务水平	——	0.998	1	1	1	1	1
风险水平	——	0.082	0.038	0.024	0	0	0
预算 $d 3$	1600	1800	2000	2200	2600	3000	3400
服务水平	——	0.996	1	0.998	0.998	1	0.996
风险水平	——	0	0	0	0	0	0
预算 $d 4$	1600	1800	2000	2200	2600	3000	3400
服务水平	1	1	1	1	1	1	1
风险水平	0	0	0	0	0	0	0
预算 $d 5$	1600	1800	2000	2200	2600	3000	3400
服务水平	——	1	1	1	1	1	1
风险水平	——	0.048	0	0	0	0	0

点击量 $g 1$	550	600	650	700	750	800
服务水平	1	1	0.988	0.981	0.974	0.910
风险水平	0	0	0	0.018	0.024	0.204
点击量 $g 2$	550	600	650	700	750	800
服务水平	1	1	0.902	——	——	——
风险水平	0	0	0	——	——	——
点击量 $g 3$	550	600	650	700	750	800
服务水平	1	1	0.984	——	——	——
风险水平	0	0	0	——	——	——
点击量 $g 4$	550	600	650	700	750	800
服务水平	1	——	——	——	——	——
风险水平	0	——	——	——	——	——
点击量 $g 5$	550	600	650	700	750	800
服务水平	1	1	1	0.964	0.944	0.940
风险水平	0	0	0.002	0.014	0.020	0.105

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Online Display Advertising Optimization Based on Guaranteed Delivery Contract under CPC Model

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