Determination of an optimal control strategies for the discrete time addictive buying model with the consumer confidence index

Abstract

In this paper, we propose a discrete addictive buying model including two controls: influencer and voucher marketing campaign in order to describe the dynamic of behavior between the classes of buyers, namely, rational buyers, excessive buyers, and addictive buyers. The model also associate with the Consumer Confidence Index (CCI) in Thailand. Identifications of consumer's buying behavior were done by fitting curve techniques based on real databases of CCI, or activity of buyers. We apply Pontryagin's maximum principle in discrete time that is used to characterize the optimal controls and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using MATLAB program.