In the face of an increasingly high-demand environment for outpatients, achieving a balance between allocation of limited medical resources and patient satisfaction has considerable social and economic benefits. Therefore, appointment scheduling (AS) system operation is used in clinics and hospitals, and its operation optimization research is of great significance. This study reviews the research progress on appointment scheduling system optimization. Firstly, we classify and conclude the existing appointment scheduling system structures and decision-making frameworks. Subsequently, we summarize the system reliability optimization framework from three aspects: appointment scheduling system optimization objectives, decision variables and constraints. Following that, we methodically review the most applied system optimization algorithms in different appointment scheduling systems. Lastly, a literature bibliometric analysis is provided. During our review of the literature, we observe that (1) optimization methods in ASs predominantly involve the application of genetic algorithms and simulation optimization algorithms; (2) neural networks and deep learning methods are core technologies in health management optimization; (3) a bibliometric analysis reveals a heightened interest in the optimization technology of ASs within China compared to other nations; and (4) further advancements are essential in the comprehensive optimization of the system, exploration of practical usage scenarios, and the application of advanced simulation and modeling techniques in this research.

Pharmaceutical supply chains face high inventory and stockout risks because of short product shelf lives and volatile demand. To enhance coordination efficiency and reduce drug waste, this study examines a two-echelon supply chain comprising a manufacturer and multiple medical institutions. We built a joint ordering and transshipment optimization model that simultaneously incorporates shelf-life constraints, the first-in–first-out (FIFO) policy, inventory capacity limits, and peer-level transshipment. Under deterministic and stochastic demand, we solved the model using Bayesian optimization and Monte Carlo simulation. The results show that moderate inventory transshipment effectively mitigates risk from demand uncertainty and increases total supply-chain profit; under stochastic demand, the optimal strategy relies more heavily on coordinated transshipment to reduce excess inventory and near-expiry waste.