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doi: 10.3934/jimo.2021219
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Uncertain KOL selection with advertising videos circulation and KOL selection diversification in advertising promotion

Meiling Jin 1, , Yufu Ning 2, , Fengming Liu 1,, , Yan Wang 1, and  Chunhua Gao 1,

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

Received  September 2021 Revised  October 2021 Early access December 2021

Fund Project: 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)

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: Uncertain programming, advertising, KOL, circulation, diversification.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Meiling Jin, Yufu Ning, Fengming Liu, Yan Wang, Chunhua Gao. Uncertain KOL selection with advertising videos circulation and KOL selection diversification in advertising promotion. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021219
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G. Panigyrakis, A. Panopoulos and E. Koronaki, All we have is words: Applying rhetoric to examine how social media marketing activities strengthen the connection between the brand and the self, International Journal of Advertising, 39 (2020), 699-718. 

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L. Liao and T. Huang, The effect of different social media marketing channels and events on movie box office: An elaboration likelihood model perspective, Information & Management, 58 (2021). 

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M. L. Cheung, G. D. Pires and P. J. Rosenberger, Investigating the role of social media marketing on value co-creation and engagement: An empirical study in China and Hong Kong, Australasian Marketing Journal, 29 (2021), 118-131. 

[14]

K. Yamagishi, L. Ocampo and D. P. Abellana, The impact of social media marketing strategies on promoting sustainability of tourism with fuzzy cognitive mapping: A case of Kalanggaman Island (Philippines), Environment, Development and Sustainability, 12 (2021), 1-33. 

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L. Xiong, V. Cho and K. M. Y. Law, A study of KOL effectiveness on brand image of skincare products, Enterprise Information Systems, 4 (2021), 1-18. 

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S. H. Jung S H and Y. J. Jeong, Twitter data analytical methodology development for prediction of start-up firms' social media marketing level, Technology in Society, 63 (2020). 

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M. L. Cheung, G. D. Pires, P. J. Rosenberger and et al., Driving COBRAs: The power of social media marketing, Marketing Intelligence & Planning, 39 (2020).

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D. M. Ibrohim, J. Widodo and S. Wahyuni, The effect of instagram as social media marketing on students' comsumtive behavior (case study of students' in faculty of economics and business university of jember from 2016 to 2019 generation), IOP Conference Series: Earth and Environmental Science, 747 (2021). 

[20]

L. Dolega, F. Rowe and E. Branagan, Going digital? The impact of social media marketing on retail website traffic, orders and sales, Journal of Retailing and Consumer Services, 4 (2015). 

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B. Ibrahim, A. Aljarah and D. Sawaftah, Linking social media marketing activities to revisit intention through brand trust and brand loyalty on the coffee shop facebook pages: Exploring sequential mediation mechanism, Sustainability, 13 (2021). 

[22]

M. C. Cohen, N. H. Z. Leung and K. Panchamgam, The impact of linear optimization on promotion planning, Oper. Res., 65 (2017), 446-468.  doi: 10.1287/opre.2016.1573.

[23]

M. C. Cohen, J. J. Kalas and G. Perakis, Promotion optimization for multiple items in supermarkets, Management Science, 67 (2021), 2340-2364. 

[24]

L. Baardman, M. C. Cohen and K. Panchamgam, Scheduling promotion vehicles to boost profits, Management Science, 65 (2019), 50-70. 

[25]

S. Ma and R. Fildes, A retail store SKU promotions optimization model for category multi-period profit maximization, European J. Oper. Res, 260 (2017), 680-692.  doi: 10.1016/j.ejor.2016.12.032.

[26]

L. Deng, W. Bi and H. Liu, A multi-stage method for joint pricing and inventory model with promotion constrains, Discrete Contin. Dyn. Syst. Ser. S, 13 (2020), 1653-1682.  doi: 10.3934/dcdss.2020097.

[27]

H. Li and Y. Yang, Optimal keywords grouping in sponsored search advertising under uncertain environments, International Journal of Electronic Commerce, 24 (2020), 107-129. 19. 

[28]

Y. Shin, S. Lee and I. Moon, Robust multiperiod inventory model with a new type of buy one get one promotion:"My Own Refrigerator", Omega, 99 (2021). 

[29]

B. Liu, Uncertainty Theory, 2$^nd$ edition, Springer-Verlag, Berlin, 2004. doi: 10.1007/978-3-540-39987-2.

[30]

B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin, 2004. doi: 10.1007/978-3-540-39987-2.

[31]

B. Liu, Some research problems in uncertainty theory, Journal of Uncertain Systems, 3 (2009), 3-10. 

[32]

S. Yu and Y. Ning, An interest-rate model with jumps for uncertain financial markets, Physica A: Statistical Mechanics and its Applications, 527 (2019), 121424.  doi: 10.1016/j.physa.2019.121424.

[33]

X. Huang and H. Di, Uncertain portfolio selection with mental accounts, International J. Systems Sci., 51 (2020), 2079-2090.  doi: 10.1080/00207721.2019.1648706.

[34]

J. Chang, L. Sun and B. Zhang, Multi-period portfolio selection with mental accounts and realistic constraints based on uncertainty theory, J. Comput. Appl. Math., 377 (2020), 112892.  doi: 10.1016/j.cam.2020.112892.

[35]

L. Xue, H. Di and X. Zhao, Uncertain portfolio selection with mental accounts and realistic constraints, J. Comput. Appl. Math., 346 (2019), 42-52.  doi: 10.1016/j.cam.2018.06.049.

[36]

B. Li and R. Zhang, A new mean-variance-entropy model for uncertain portfolio optimization with liquidity and diversification, Chaos, Solitons & Fractals, 146 (2021), 110842.  doi: 10.1016/j.chaos.2021.110842.

[37]

Y. Li, R. Peng and I. Kucukkoc, System reliability optimization for an assembly line under uncertain random environment, Computers & Industrial Engineering, 146 (2020). 

[38]

Y. Ning and T. Su, A multilevel approach for modelling vehicle routing problem with uncertain travelling time, J. Intelligent Manufacturing, 28 (2017). 

[39]

Y. Ning, N. Pang and X. Wang, An uncertain aggregate production planning model considering investment in vegetable preservation technology, Math. Probl. Eng., 2019 (2019), 8505868.  doi: 10.1155/2019/8505868.

[40]

M. Jin, Y. Ning and B. Li, Uncertain KOL selection with multiple constraints in advertising promotion, IEEE Access, 9 (2021), 142839-142878. 

[41]

F. Atigan, A survey research on the effects of sales promotion, and advertising and store image on customers buying behavior in retailing, Pressacademia, 11 (2020), 121-126. 

show all references

References:
[1]

P. Vijayalakshmi, A study on social media marketing podcast of food and beverage brands with reference to Tamilnadu, Review of Research Journal, 4 (2015). 

[2]

C. I. Enyinda, A. P. Opute and A. Fadahunsi, Marketing-sales-service interface and social media marketing influence on B2B sales process, Journal of Business & Industrial Marketing, 36 (2020). 

[3]

R. Eid, Z. Abdelmoety and G. Agag, Antecedents and consequences of social media marketing use: an empirical study of the UK exporting B2B SMEs, Journal of Business & Industrial Marketing, 4 (2019). 

[4]

J. Syaifullah, M. Syaifudin and M. U. Sukendar, Social Media Marketing and Business Performance of MSMEs During the COVID-19 Pandemic, The Journal of Asian Finance, Economics, and Business, 8 (2021), 523-531. 

[5]

B. Melovic, D. Cirovic and B. Dudic, The analysis of marketing factors influencing consumers' preferences and acceptance of organic food products - Recommendations for the optimization of the offer in a developing market, Foods, 9 (2020). 

[6]

A. Capatina, M. Kachour, J. Lichy and et al., Matching the future capabilities of an artificial intelligence-based software for social media marketing with potential users' expectations, Technological Forecasting and Social Change, 151 (2021), StartingPage–EndingPage.

[7]

A. Wibowo, S. C. Chen and U. Wiangin, Customer behavior as an outcome of social media marketing: The role of social media marketing activity and customer experience, Sustainability, 13 (2021). 

[8]

G. Panigyrakis, A. Panopoulos and E. Koronaki, All we have is words: Applying rhetoric to examine how social media marketing activities strengthen the connection between the brand and the self, International Journal of Advertising, 39 (2020), 699-718. 

[9]

A. Puspaningrum, Social media marketing and brand loyalty: The role of brand trust, The Journal of Asian Finance, Economics, and Business, 7 (2020), 951-958. 

[10]

H. B. K. Nobar, H. K. Kalejahi and R. Rostamzadeh, Impact of social media marketing activities on brand equity and brand commitment in the leather industry, International Journal of Business Excellence, 20 (2020), 191-204. 

[11]

L. Liao and T. Huang, The effect of different social media marketing channels and events on movie box office: An elaboration likelihood model perspective, Information & Management, 58 (2021). 

[12]

S. F. Salem and S. O. Salem, Effects of social media marketing and selected marketing constructs on stages of brand loyalty, Global Business Review, 22 (2021), 650-673. 

[13]

M. L. Cheung, G. D. Pires and P. J. Rosenberger, Investigating the role of social media marketing on value co-creation and engagement: An empirical study in China and Hong Kong, Australasian Marketing Journal, 29 (2021), 118-131. 

[14]

K. Yamagishi, L. Ocampo and D. P. Abellana, The impact of social media marketing strategies on promoting sustainability of tourism with fuzzy cognitive mapping: A case of Kalanggaman Island (Philippines), Environment, Development and Sustainability, 12 (2021), 1-33. 

[15]

N. Izakova, L. Kapustina and A. Drevalev, Performance of social media marketing communications of industrial companies, SHS Web of Conferences. EDP Sciences, 93 (2021), 1-16. 

[16]

L. Xiong, V. Cho and K. M. Y. Law, A study of KOL effectiveness on brand image of skincare products, Enterprise Information Systems, 4 (2021), 1-18. 

[17]

S. H. Jung S H and Y. J. Jeong, Twitter data analytical methodology development for prediction of start-up firms' social media marketing level, Technology in Society, 63 (2020). 

[18]

M. L. Cheung, G. D. Pires, P. J. Rosenberger and et al., Driving COBRAs: The power of social media marketing, Marketing Intelligence & Planning, 39 (2020).

[19]

D. M. Ibrohim, J. Widodo and S. Wahyuni, The effect of instagram as social media marketing on students' comsumtive behavior (case study of students' in faculty of economics and business university of jember from 2016 to 2019 generation), IOP Conference Series: Earth and Environmental Science, 747 (2021). 

[20]

L. Dolega, F. Rowe and E. Branagan, Going digital? The impact of social media marketing on retail website traffic, orders and sales, Journal of Retailing and Consumer Services, 4 (2015). 

[21]

B. Ibrahim, A. Aljarah and D. Sawaftah, Linking social media marketing activities to revisit intention through brand trust and brand loyalty on the coffee shop facebook pages: Exploring sequential mediation mechanism, Sustainability, 13 (2021). 

[22]

M. C. Cohen, N. H. Z. Leung and K. Panchamgam, The impact of linear optimization on promotion planning, Oper. Res., 65 (2017), 446-468.  doi: 10.1287/opre.2016.1573.

[23]

M. C. Cohen, J. J. Kalas and G. Perakis, Promotion optimization for multiple items in supermarkets, Management Science, 67 (2021), 2340-2364. 

[24]

L. Baardman, M. C. Cohen and K. Panchamgam, Scheduling promotion vehicles to boost profits, Management Science, 65 (2019), 50-70. 

[25]

S. Ma and R. Fildes, A retail store SKU promotions optimization model for category multi-period profit maximization, European J. Oper. Res, 260 (2017), 680-692.  doi: 10.1016/j.ejor.2016.12.032.

[26]

L. Deng, W. Bi and H. Liu, A multi-stage method for joint pricing and inventory model with promotion constrains, Discrete Contin. Dyn. Syst. Ser. S, 13 (2020), 1653-1682.  doi: 10.3934/dcdss.2020097.

[27]

H. Li and Y. Yang, Optimal keywords grouping in sponsored search advertising under uncertain environments, International Journal of Electronic Commerce, 24 (2020), 107-129. 19. 

[28]

Y. Shin, S. Lee and I. Moon, Robust multiperiod inventory model with a new type of buy one get one promotion:"My Own Refrigerator", Omega, 99 (2021). 

[29]

B. Liu, Uncertainty Theory, 2$^nd$ edition, Springer-Verlag, Berlin, 2004. doi: 10.1007/978-3-540-39987-2.

[30]

B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin, 2004. doi: 10.1007/978-3-540-39987-2.

[31]

B. Liu, Some research problems in uncertainty theory, Journal of Uncertain Systems, 3 (2009), 3-10. 

[32]

S. Yu and Y. Ning, An interest-rate model with jumps for uncertain financial markets, Physica A: Statistical Mechanics and its Applications, 527 (2019), 121424.  doi: 10.1016/j.physa.2019.121424.

[33]

X. Huang and H. Di, Uncertain portfolio selection with mental accounts, International J. Systems Sci., 51 (2020), 2079-2090.  doi: 10.1080/00207721.2019.1648706.

[34]

J. Chang, L. Sun and B. Zhang, Multi-period portfolio selection with mental accounts and realistic constraints based on uncertainty theory, J. Comput. Appl. Math., 377 (2020), 112892.  doi: 10.1016/j.cam.2020.112892.

[35]

L. Xue, H. Di and X. Zhao, Uncertain portfolio selection with mental accounts and realistic constraints, J. Comput. Appl. Math., 346 (2019), 42-52.  doi: 10.1016/j.cam.2018.06.049.

[36]

B. Li and R. Zhang, A new mean-variance-entropy model for uncertain portfolio optimization with liquidity and diversification, Chaos, Solitons & Fractals, 146 (2021), 110842.  doi: 10.1016/j.chaos.2021.110842.

[37]

Y. Li, R. Peng and I. Kucukkoc, System reliability optimization for an assembly line under uncertain random environment, Computers & Industrial Engineering, 146 (2020). 

[38]

Y. Ning and T. Su, A multilevel approach for modelling vehicle routing problem with uncertain travelling time, J. Intelligent Manufacturing, 28 (2017). 

[39]

Y. Ning, N. Pang and X. Wang, An uncertain aggregate production planning model considering investment in vegetable preservation technology, Math. Probl. Eng., 2019 (2019), 8505868.  doi: 10.1155/2019/8505868.

[40]

M. Jin, Y. Ning and B. Li, Uncertain KOL selection with multiple constraints in advertising promotion, IEEE Access, 9 (2021), 142839-142878. 

[41]

F. Atigan, A survey research on the effects of sales promotion, and advertising and store image on customers buying behavior in retailing, Pressacademia, 11 (2020), 121-126. 

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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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
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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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
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
Table Options

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$ 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
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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$ 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
Table 5.  Parameters value
$ k $ $ \varepsilon $ $ v $
0.015 0.0001 0.81
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$ k $ $ \varepsilon $ $ v $
0.015 0.0001 0.81
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
Table Options

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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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