Uncertain KOL selection with advertising videos circulation and KOL selection diversification in advertising promotion

Meiling Jin; Yufu Ning; Fengming Liu; Yan Wang; Chunhua Gao

doi:10.3934/jimo.2021219

Article Contents

2023, Volume 19, Issue 2: 1058-1083. Doi: 10.3934/jimo.2021219

This issue Previous Article Sufficient optimality conditions and Mond-Weir duality results for a fractional multiobjective optimization problem Next Article

Uncertain KOL selection with advertising videos circulation and KOL selection diversification in advertising promotion

1.
Business School, Shandong Normal University, Jinan, 250014, China
2.
School of Information Engineering, Shandong Youth University of Political Science, Key Laboratory of Intelligent Information Processing, Technology and Security in Universities of Shandong, Jinan, 250103, China

^*Corresponding author: Fengming Liu
^*Corresponding author: Fengming Liu

Received: August 31, 2021

Revised: September 30, 2021

Early access: December 2021

Published: February 2023

This research was supported in part by the National Social Science Foundation of China (No. 14BTQ049, 21BGL001), the National Natural Science Foundation of China(71701115), Shandong Natural Science Foundation (ZR2020MG003), Special Project for Internet Development of Social Science Planning Special Program of Shandong Province (17CHLJ23)

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Abstract

Social media marketing is the mainstream marketing method. Before the launch of a new product, the company will advertise on social platforms. A major problem is how to reasonably arrange KOL (Key Opinion Leader) for advertising promotion in order to achieve the results that the company wants. At this time, KOL selection optimization is an effective method to make the best advertising promotion decision for decision-makers. In addition, the uncertainty in advertising promotion has brought challenges for KOL selection. Therefore, in the absence of historical promotion data, this paper solves the uncertainty of advertising promotion in social media marketing. Taking MCN (Multi-Channel-Network) as the decision maker, maximizing the advertising promotion effect as the goal, considering a variety of realistic constraints and uncertain factors in advertising promotion, the optimal allocation of KOL in advertising promotion is realized by constructing an uncertain chance-constrained programming model. Then, by solving the clear form of the model, the optimal solution of the model is obtained. Finally, the effectiveness of the model is verified by numerical examples, and the effects of KOL selection diversification and advertising video circulation on advertising promotion are discussed, which provides decision support for decision-makers.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. Fmincon's iterative convergence graph of objective function value

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Figure 2. The graph of OFV changing with$ v $

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Figure 3. The graph of Relative Risk changing with$ v $

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Figure 4. The graph of OFV changing with$ k $

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Figure 5. The graph of Relative Risk changing with$ k $

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Figure 6. Fmincon's iterative convergence graph of Objective Function Value

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Table 1. Main uncertain parameters

Level $ i $	$ {{\mu }_{i}} $	$ {{\sigma }_{i}} $	$ {{e}_{i}} $	$ {{\delta }_{i}} $	$ {{a}_{i}} $	$ {{b}_{i}} $
1	26000	50	3000	33	0.011	0.019
2	51000	100	4500	87	0.009	0.024
3	100000	150	9900	57	0.007	0.016
4	340000	300	19000	75	0.013	0.032
5	1100000	350	120000	89	0.008	0.015
6	8700000	500	780000	96	.008	0.025
7	15000000	800	1400000	125	0.006	0.031
8	37000000	1000	2900000	200	0.005	0.026

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Table 2. Allocation ratio

Level $ i $	Allocation ratio
1	0.0000
2	0.0000
3	0.0000
4	0.1909
5	0.0000
6	0.0000
7	0.0000
8	0.8091

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Table 3. The Influence of KOL Selection Diversification on Advertising Promotion

$ v $	0.51	0.61	0.71	0.81	0.91
$ OFVe $	3.0946e+04	3.2739e+04	3.4947e+04	3.7714e+04	4.1310e+04
$ OFVr $	3.5142e+03	3.8804e+03	4.33e+03	4.8971e+03	5.6126e+3
Relative Risk	0.4178	0.4360	0.4562	0.4777	0.4998

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Table 4. The Influence of Video Circulation on Advertising Promotion

$ k $	0.13	0.15	0.17	0.19	0.21
$ OFVe $	2.59618e+04	2.59620e+04	5.09250e+04	5.09265e+04	5.09270e+04
$ OFVr $	2.5001e+03	2.5001e+03	1.3611e+04	3.3611e+04	6.2500e+04
Relative Risk	0.354265	0.354262	0.267275	0.659990	1.227247

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Table 5. Parameters value

$ k $	$ \varepsilon $	$ v $
0.015	0.0001	0.81

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Table 6. Allocation ratio

Level $ i $	Allocation ratio
1	0.0395
2	0.0407
3	0.0387
4	0.0488
5	0.0172
6	0.0067
7	0.0005
8	0.8079

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