Paolo Latorre, Armando Meza, Héctor López-Ospina, Wouter Verbeke, Juan Pérez
Abstract
Designing profitable customer retention campaigns requires a prescriptive approach to jointly optimize who to target and what incentive to offer. This paper presents a prescriptive analytics framework that solves this joint optimization problem. We model the acceptance probability of the campaign as an explicit function of the incentive and derive optimality conditions, including a closed form in the linear case and a uniqueness result under a mild slope bound in the logistic case. We state and prove these results for both a linear response and a logistic (sigmoid) response, jointly optimizing the targeting threshold and the incentive level. We instantiate the approach with a transparent Mamdani fuzzy inference system to assess churn risk, while the prescriptive layer remains predictor-agnostic. On a public telecommunications dataset, we evaluate the framework on a 75/25 train and test split across several predictors (Mamdani FIS, logistic regression, random forest, Naive Bayes, and XGBoost) and incentive acceptance families (linear; sigmoids with different slopes, shifts, and ceilings). Using the same prescriptive layer (targeting threshold and acceptance curve), the test-set results show consistent profit gains; the best outcome is obtained with gradient-boosted trees combined with a sigmoid. These findings confirm that the proposed framework is predictor-agnostic and practically generalizable across scoring models.
