A fuzzy mathematical programming approach for cross-sell optimization in retail banking

We consider the problem of selecting the optimal list of customers to target for a cross-sell campaign in a retail bank. Target selection involves taking estimates of several parameters (response propensity, expected volume, expected profit from a customer, etc) and deciding on the list of customers to whom the offer should be sent such that a certain set of business objectives are met/optimized. We discuss some of the issues related to the target selection process, namely those of unreliable estimates and computational complexity of the problem. We propose a fuzzy mathematical programming technique to address these issues. The imprecise parameters and constraints are represented as triangular fuzzy numbers, while the problem of computational complexity is addressed through a group-level formulation. We use an example of a real-life cross-sell problem for a bank to demonstrate the method. We also provide some sensitivity analyses on critical resources.