Stability analysis and optimal strategies for controlling a boycotting behavior of a commercial product

Iranian Journal of Numerical Analysis and Optimization

مقاله 4، دوره 14، Issue 3 - شماره پیاپی 30، آذر 2024، صفحه 708-735   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.86892.1394

نویسندگان

O. Aarabate^* ؛ S. Belhdid؛ O. Balatif

Laboratory of Fundamental Mathematics and their Applications, Department of Mathematics, Faculty of Sciences, University of Chouaib Doukkali, El jadida, Morocco.

چکیده

In this work, we propose a mathematical model that describes citizens’ be-havior toward a product, where individuals are generally divided into three main categories: potential consumers, boycotters who abstain from it for various reasons, and actual consumers. Therefore, our work contributes to understanding product boycott behavior and the factors influencing this phenomenon. Additionally, it proposes optimal strategies to control boy-cott behavior and limit its spread, thus protecting product marketing and encouraging consumer reuse. We use mathematical theoretical analysis to study the local and global stability, as well as sensitivity analysis to identify parameters with a high impact on the reproduction number R0. Subsequently, we formulate an optimal control problem aimed at minimizing the number of boycotters and maximizing consumer participation. Pontryagin’s maximum principle is employed to characterize the optimal controls. Finally, numerical sim-ulations conducted using MATLAB confirm our theoretical results, with a specific application to the case of the boycott of Centrale Danone by several Moroccan citizens in April 2018.

کلیدواژه‌ها

Modeling a boycott behavior؛ Local and global stability؛ Sensi-tivity analysis؛ Optimal control problem

مراجع

[1] Albayati, M.S., Mat, N.K.N., Musaibah, A.S., Aldhaafri, H.S. and Al-matari, E.M. Participate in boycott activities toward danish products from the perspective of Muslim consumer, Am. J. Econ. Special Issue (2012), 120–124.
[2] Balatif, O., Khajji, B. and Rachik, M. Mathematical modeling, analysis, and optimal control of abstinence behavior of registration on the electoral lists, Discrete Dyn. Nature Soc. 2020 (2020).
[3] Boyce, W.E. and DiPrima, R.C. Elementary differential equations and boundary value problems, John Wiley and Sons, New York, NY, USA, 2009.
[4] Braunsberger, K. and Buckler, B. What motivates consumers to partici-pate in boycotts: Lessons from the ongoing Canadian seafood boycott, J. Bus. Res. 64(3) (2011), 96–102.
[5] Diermeier, D. and Van Mieghem, J.A. Voting with your Pocketbook-A Stochastic Model of Consumer Boycotts, Math. Comput. Model. 48 (2008), 1497–1509.
[6] Edelstein-Keshet, L. Mathematical Models in Biology, SIAM, 1988.
[7] EL Arraf, S. and Biddou, N. Corporate Response and Responsibility in the case of consumer boycotts: an Analysis of Centrale Danone crisis in Morocco, Journal d’Economie, de Management, d’Environnement et de Droit, 2(2) (2019), 29–30.
[8] Fleming, W.H. and Rishel, R.W. Deterministic and Stochastic Optimal Control, Springer, New York, NY, USA, 1975.
[9] Hoffmann, S. Are boycott motives rationalizations?, J. Consum. Behav. 12(3) (2013), 214–222.

[10] Indicateurs-Sociaux-ar [online]. The Ministry of Economy and Finance, (2018). Available from: https://www.finances.gov.ma, (access date : 9 January 2024).
[11] Klein, J.G., Smith, N.C. and John, A. Why We Boycott: Consumer Motivations for Boycott Participation, J. Mark. 68(3) (2004), 92–109.
[12] LaSalle, J.P. The stability of dynamical systems, Regional Conference Series in Applied Mathematics Vol. 25, SIAM. Philadelphia, PA, USA, 1976.
[13] Li, C. and Ma, Z. Dynamics analysis of a mathematical model for new product innovation diffusion, Discrete Dyn. Nature Soc. 2020 (2020), 13 pages.
[14] Makinde, O.D. and Okosun, K.O. Impact of chemo-therapy on optimal control of malaria disease with infected immigrants, Biosystems 104(1) (2011), 32–41.
[15] Mayo, C.C. Captain Boycott 1832-1897 [online]. Comhairle Contae Mhaigh Eo Mayo County Council, (2006). Available
from: https://www.mayo.ie/discover/history-heritage/ great-battles-conflicts/captain-boycott, (access date : 9 January 2024).
[16] Mesbah, M. “Khalih Yreeb”: Boycott campaign and empowering the role of ordinary citizen [online]. Moroccan Institute For Policy Analy-sis. Available from: https://mipa.institute/6734, (access date : 11 January 2024).
[17] Mosameh, M. The boycott campaign for Central products loses “15 billion centimeters” [online]. Berrechid news, (6 April 2018). Available from: https://www.berrechidnews.com/2018/06/5074.html, (access date : 01 January 2024).
[18] Nakul, C., Cushing J.M. and Hyman, J.M. Bifurcation analysis of a mathematical model for malaria transmission, SIAM J. Appl. Math. 67(1) (2006), 24–45.

[19] Neilson, L.A. Boycott or buycott? Understanding political consumerism, J. Consum. Behav. 9(3) (2010), 214–227.
[20] News note for the high commission for planning about the basic char-acteristics of an active, working population During the year 2018, High Commission for Planning, (2018). Available from: https://www.hcp. ma/region-drda.
[21] Palacios-Florencio, B., Revilla-Camacho, M.A., Garzón, D. and Prado-Román, C. Explaining the boycott behavior: A conceptual model proposal and validation, J. Consum. Behav. 20(5) (2021), 1313–1325.
[22] Pontryagin, L.S., Boltyanskii, V.G. Gamkrelidze, R.V. and Mishchenko, E.F. The mathematical theory of optimal processes, Wiley, New York, NY, USA, 1962.
[23] Zhuo, C., Chen S. and Yan, H. Mathematical modelling of B2C consumer product supply strategy based on nonessential demand pattern, J. Math. 2024 (2024), 14 pages.
[24] Zhuo, Z., Chau K.Y., Huang, S. and Kit Ip, Y. Mathematical modeling of optimal product supply strategies for manufacturer-to-group customers based on semi-real demand patterns, Int. J. Eng. Bus. Manag. 12 (2020),1–8.
[25] Zhuo, Z., Chen, S., Yan, H. and He, Y. A new demand function graph: Analysis of retailer-to-individual customer product supply strategies un-der a non-essential demand pattern, Plos one 19(2) (2024), e0298381.