Evaluation Timing with Dynamic Information: Optimization and Heuristic

Product evaluation is an essential business process, and digital innovation has made it possible for companies to immediately process available information. We develop a model where a company continuously assesses information that follows a doubly stochastic Poisson process with a mean-reverting and stochastic intensity. Accordingly, the company faces a two-dimensional optimal stopping problem in which the company continues to evaluate the product if and only if the product reputation and information intensity remain in a continuation set. We employ a probabilistic approach to prove that the continuation set takes the form of an open interval for any fixed information arrival intensity. Given the complicated nature of the optimal solutions, we develop an asymptotic expansive solution, and numerical studies show that our solution performs well. We also analyze a heuristic solution where the company substitutes the dynamic intensity with a constant intensity. Interestingly, we find that this heuristic company does not necessarily benefit from having a higher product reputation.