Robust analysis on promotion duration for two competitive brands

There are few studies that provide a useful tool or model to determine the promotion duration during the transition state of customers' switching between different brands. This implies that marketing managers usually decide the promotion duration based on their past experiences. The study integrates the Markov chain, entropy, and diffusion theory to model the problem and find a solution. Furthermore, the Taguchi method is also used to capture the uncertain parameters of the model to solve the problem. A numerical example is used to illustrate how the model determines optimal promotion duration.