A Bayesian Framework for Optimal Pricing Incorporating Business Rules

Business rules have become an important part of the practice of price optimization systems. These rules are meant to capture managerial knowledge and insights that impose important constraints on the pricing problem. Traditional approaches to price optimization take a two-step approach to setting prices. First, a sales response model is specified, and the parameters are estimated given an observed dataset. Second, this model is used for inference to make decisions about the optimal price. Often the optimal pricing solutions from the estimated sales response model are nonsense suggesting prices that are unfairly high, which leads the manager to impose a set of post hoc constraints on the feasible price space to find a more appropriate solution. We argue that manager’s constraints on the price solution represent prior information about the model. We show that incorporating this information post hoc instead of a priori leads to inefficient pricing decisions. To facilitate the creation of the model and its prior we show how constraints implied by business rules and statements about optimal prices can be translated into informative prior distributions. These prior distributions appropriately weight the managerial knowledge against the data unlike the traditional approach. We also consider situations in which the analyst may not know either the business rule or model with complete certainty and illustrate the impact of this uncertainty on the optimal pricing solution. In summary, our Bayesian method improves the quality of the pricing decisions made by managers and offers a consistent and scientific approach for incorporating managerial expertise into the pricing problem.