A methodology based on profitability criteria for defining the partial defection of customers in non-contractual settings

•We propose a methodology for optimizing the selection of a churn definition in a firm.•Each churn definition is evaluated using two economic measures: profit and return.•The definition maximizing profit and return is selected by multiobjective programming.•The cost that the firm should invest per client to preventing churn is also optimized.•A big real database has been used for numerical experiments with satisfactory results. The defection or churn of customers represents an important concern for any company and a central matter of interest in customer base analysis. An additional complication arises in non-contractual settings, where the characteristics that should be observed to saying that a customer has totally or partially defected are not clearly defined. As a matter of fact, different definitions of the churn situation could be used in this context. Focusing on non-contractual settings, in this paper we propose a methodology for evaluating the short-time economic effects that using a certain definition of churn would have on a company. With this aim, we have defined two efficiency measures for the economic results of a marketing campaign implemented against churn, and these measures have been computed using a set of definitions of partial defection. Our methodology finds that definition maximizing both efficiency measures and moreover, the monetary amount that the company should invest per customer in the campaign for achieving the optimal solution. This has been modelled as a multiobjective optimization problem that we solved using compromise programming. Numerical results using real data from a Spanish retailing company are presented and discussed in order to show the performance and validity of our proposal.