Optimal Pricing and Production Planning for Subscription-Based Products

In this paper, we address the problem of a magazine publishing firm facing stochastic demand over multiple periods. We model the dynamics of customer subscription and retention/attrition. We identify the key decision variables to enhance magazine profitability: production quantity, subscription price, and newsstand price. First, we provide a dynamic programming formulation of the firm's problem and then propose a single-stage reduction that admits a classical newsvendor characterization. For both the finite and infinite horizon cases, we characterize the optimal policy of the firm where the decision variables are one, two, or all three of the aforementioned variables. Next, we consider the duopolistic setting, where firms benefit from the overflow of the competitor's unmet demand, and we provide analytic solutions in the case of uniform demand distributions. Finally, we report on computational experiments in both monopolistic and duopolistic settings and provide managerial insights.