Dynamic Scheduling of Recurring Multisession Appointments with Heterogeneous Clients

Clients seeking paramedical and rehabilitation services require recurring treatment sessions over an extended period. Unlike single-visit problems, these services must assign each accepted client to a fixed, recurring day–time slot that remains occupied throughout the treatment program. This structure creates long-term capacity commitments that limit future scheduling flexibility and complicate acceptance decisions, particularly when clients differ in availability and required program durations. Motivated by an early intervention program for infants and toddlers with developmental delays, we study scheduling policies designed to address this combination of heterogeneity, uncertainty, and recurrence constraints. We model the multisession appointment scheduling problem as a Markov decision process in which requests arrive sequentially and decisions must consider both immediate feasibility and the long-term implications of blocking a slot across many periods. Our analysis identifies key structural elements of the scheduling decision, including a slot-selection guideline that assigns accepted clients to the least popular feasible slot and a duration-based threshold that characterizes acceptance behavior. These insights highlight the value of preserving flexibility and anticipating demand when scheduling recurring appointments under uncertainty. Building on these results, we develop a heuristic that groups schedule states into occupancy categories and applies simplified acceptance thresholds. Computational experiments show that this anticipatory approach outperforms first come, first served benchmarks, particularly when slot popularity is uneven or program durations vary widely. Whereas we do not model health outcomes directly, prior research links improved access, timely initiation, and continuity of care with better therapeutic results, underscoring the broader potential impact of more efficient scheduling.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/serv.2026.0025 .