HEC Research Papers Series,
HEC Paris

Abstract: Firms seeking to grow their customer base must attract new customers while retaining and serving existing ones, often under limited operational capacity. These decisions are further complicated by uncertainty about how customers respond to prices, acquisition efforts, and retention initiatives. Firms therefore face a customer-growth problem in which marketing and operational decisions must be coordinated while customer behavior is learned over time. We develop a dynamic framework that jointly integrates pricing, customer acquisition, customer retention, operational capacity, and behavioral learning. The model tracks the evolution of potential and existing customer pools under changing market conditions and allows both customer demand and customer-transition behavior to be learned nonparametrically from observed interactions. To solve the resulting problem, we propose a three-stage learning architecture consisting of unconstrained experimentation, capacity-aware refinement, and policy deployment. Our analysis establishes finite-time performance guarantees for the proposed procedure. We show that cumulative profit loss from learning, relative to a benchmark with full knowledge of customer behavior, grows sublinearly with the planning horizon, so that average performance loss converges to zero over time. We further characterize how firms should allocate time across the three stages and show that operational capacity can be incorporated without changing the order of the regret guarantee while maintaining near-feasibility throughout the learning process. These results demonstrate that firms can learn how to grow and manage their customer base while progressively adapting their decisions to operational limitations, without incurring substantial long-run performance losses.

Keywords: Customer relationship management; acquisition and retention; nonparametric online learning; capacity constraints; revenue management; contextual bandits; operations research in marketing

JEL-codes: C44; C61; D83; M11; M31

47 pages, October 7, 2026

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