Recently, Internet of Things (IoT) technology has become popular and applicable in different fields. The exchangeable data through IoT systems are extremely huge. This poses a great challenge in constructing a scalable and reliable computing scheme for IoT environments. Therefore, an efficient computing scheme for an IoT-enabled healthcare environment was proposed in this paper. The computing scheme idea was based on the use of cloud, fog, mist and edge computing strategies after dividing their resources into N-tiers. For easy management, these tiers were clustered depending on their geographical distribution. The number of tiers for each computing strategy dynamically changed depending on the computing load. Each tier had its own capabilities. Therefore, selecting a computing strategy and its tier was achieved regarding the data requirements and the specs of each computing resource. To evaluate the proposed computing scheme, a network simulator package (NS-3) was used to construct a simulation for the IoT-enabled healthcare environment and the computing scheme. Most simulation results of our computing scheme were compared with the cloud/fog/mist, cloud/fog and cloud computing schemes. Finally, the simulation results proved that the proposed computing scheme outperformed the performance of other traditional computing schemes regarding the following performance metrics: Delay, utilization, energy consumption, beneficial users and different healthcare organization complexities.