Automated drug dispensing systems (ADDSs) are increasingly in demand in today's pharmacies, primarily driven by the growing ageing population. Recognizing the practical challenges faced by pharmacies implementing ADDSs, this study aims to optimize the layout design and sequencing issues within a human-machine cooperation environment to enhance the system throughput of ADDSs. Specifically, we develop models for drug retrieval sequencing under different system layout designs, taking into account the stochastic sorting time of pharmacists. The prescription order arrival pattern follows a successive arrival mode. To assess the efficiency of ADDSs with one input/output point and two input/output points, we propose dual command retrieval sequencing models that optimize the retrieval sequence of drugs in adjacent prescription orders. Notably, our models incorporate the stochastic sorting time of pharmacists to analyze its impact on ADDS performance. Through experimental comparisons of average picking times for prescription orders under various operational conditions, we demonstrate that a system layout design incorporating two input/output points significantly enhances the efficiency of prescription order fulfilment within a human-machine cooperation environment. Furthermore, our proposed retrieval sequencing method outperforms dynamic programming, greedy, and random strategies in terms of improving prescription order-picking efficiency. By addressing the layout design and sequencing challenges, our research contributes to the field of intelligent warehousing, particularly in smart pharmacies. The findings provide valuable insights for healthcare facilities and organizations seeking to optimize ADDS performance and enhance drug dispensing efficiency.