Content Rotation in the Presence of Satiation Effect

Service providers often employ rotational schedules for offerings, such as weekly TV series updates or periodic special events in video games. These rotations not only reduce the operating costs associated with constant offerings, but also moderate consumer satiation caused by frequent consumption of the same product. Despite the prevalence of simple designs in practice, there is a lack of guidance on designing effective rotational schedules. In this paper, we explore the design of rotational schedules for service providers to maximize long-run average profits. We develop an analytical model based on utility theory, which connects consumer consumption with satiation and product correlation. Our investigation encompasses various scenarios, including single product offerings, regular and rotational product pairs, and multiple product assortments. For a single product, we characterize the optimal frequency. For a regular and rotational product pair, we observe an interesting ripple effect in consumer dynamics. In this case, we analyze the optimal frequency and choice of the rotational product, which depend on reciprocal influences between the two products. In scenarios with multiple products, we demonstrate that as the number of products increases, the assortment depth converges to a constant, and the cycle length should grow linearly. Furthermore, we find that product permutations have a marginal impact on total consumption. To address general situations, we introduce a numerical method based on mixed-integer programming and conduct numerical studies using both synthetic and real data. Our findings and insights offer a first step towards understanding the design of content rotation.