This work is motivated by the appointment booking of specialist services at the ambulatory care center (ACC) in a major public hospital in Hong Kong. We study scheduling policies in a healthcare system in which patients' waiting times for medical consultations are governed by the Hong Kong Hospital Authority. Specifically, the ACC accepts only advanced bookings, and patients should receive consultation within a stipulated target waiting time. We study two forms of scheduling: allocation scheduling and advance scheduling. The decisions involved in the former are consultation quotas for each day, and the choices of the latter regard the specific consultation date for each patient. These two scheduling problems can be formulated as discrete-time, finite horizon MDPs. Although with several structural properties being developed for the optimal policies, the cure of dimensionality remains. We then resort to the approximate dynamic programming (ADP) approach for allocation scheduling. For the advance scheduling problem, we propose a heuristic policy which is optimal when the waiting time target is within 2 periods. Numerical experiments are conducted to evaluate the performance of heuristic policies. The results show that for most of the settings, our proposed heuristics outperforms several known policies implemented in practice.