How to compute optimal catalog mailing decisions

We develop, estimate, and test a response model of order timing and order volume decisions of catalog customers and derive a Bayes rule for optimal mailing strategies. The model integrates the when and how much components of the response; incorporates the mailing decision of the firm; and uses a Bayesian framework to determine the optimal mailing rule for each catalog customer. The Bayes rule we propose for optimal mailing strategy allows for a broad set of objectives to be realized across the time horizon, such as profit maximization, customer retention, and utility maximization with or without risk aversion. We find that optimizing the objective function over multiple periods as opposed to a single period leads to higher expected profits and expected utility. Our results indicate that the cataloguer is well advised to send fewer catalogs than its current practice in order to maximize expected profits and utility.