•The replenishment process is crucial to performance in central fill pharmacies.•A continuous-time Markov Chain models the stochastic behavior of replenishment.•Developed Markov Chain can be appropriately used to analyze replenishment process.•Reorder point, canister size, number of operators can be optimized to reduce cost.•Proposed approach can be extended to large-scale dispensing systems. This study focuses on the replenishment process of the robotic dispensing system (RDS) in a central fill pharmacy (CFP). The RDS is capable of autonomously counting and filling tens of thousands of prescription orders each day while being replenished by operators. If the replenishment is not completed on time and the dispenser becomes empty while orders continue to arrive, the RDS will experience a problem called a rundry error and cannot fill orders until the replenishment is complete. Because rundry errors significantly degrade the performance of CFPs, there is an urgent need to analyze and understand the replenishment process of the RDS to prevent these errors. The main objective of this study is to develop a systematic approach to model the stochastic behavior of the replenishment process by using a continuous-time Markov Chain and to find the optimal reorder point (ROP), canister size, and the number of operators that minimize the replenishment costs. Numerical experiment results show that ROP, canister size, and the number of operators have a significant effect on the performance of the RDS. In the dispenser analyzed in this study, increasing the ROP from 0.5 to 0.5 led to a 26.7% reduction in downtime and a 49.2% reduction in total costs. Similarly, Increasing the canister size from a 0.5-L canister to a 2-L canister led to a 10.5% reduction in downtime and a 69.5% reduction in total costs. The results show that the proposed approach can be used to optimize the replenishment process to minimize cost.