This paper presents two families of heuristic algorithms for scheduling medications that interact with each other. All algorithms accept as input machine readable medication directions that specify the dose size and timing constraints to be met by all schedules. One family of algorithms is called One-Medication-at-a-Time, or O MAT. As the name implies, an OMAT algorithm produces a full schedule for each of the user's medication in turn. Algorithms in the other family are called One-Dose-at-a-Time {ODAT) algorithms. An OD AT algorithm schedules one dose at a time without prior knowledge, or with limited knowledge, about future doses. It may fail to make good scheduling decisions compared with OMAT algorithms but can better accommodate dynamic variations in user behavior. Both OMAT and ODAT algorithms apply a variety of priority assignments as well refinements such as letting the user take medications as soon as possible or as late as possible. Simulation results on their performance in terms of success rate and schedule quality can help builders of smart medication dispensers and scheduling tools choose among algorithms and tradeoff merits along different dimensions.