Optimization study of three-stage assembly flowshop problem in pharmacy automation dispensing systems

Abstract

Along with the rising prevalence of chronic diseases and the increasing complexity of pharmaceutical care, pharmacy automation dispensing systems (PADS)s are utilized to improve the quality of patient care, reduce dispensing-related medication errors, and cut down medication-related expenses. After PADSs fulfill prescription orders, patients still have to dispense medications for each meal by themselves. It is well known that dispensing medications is time-consuming and exhausting, especially for chronic patients. During the manual dispensing process, some unexpected medical errors might appear, which would result in discomfort, harm, and even death. To provide efficient and patient-centered pharmacy care, we proposed automatically dispensing prescriptions by meal orders in PADS. Specifically, we formulated a novel three-stage assembly flowshop problem to fulfill prescription orders at the level of meal orders to minimize the total completion times of packing prescription orders. In our studied PADS, there are fully flexible parallel machines dispensing medication jobs and collating sub-orders (meal prescription orders) in the first and second stages, and one assembly machine packing prescription orders in the third stage. Based on the properties of the optimal schedule, we proposed a branch-and-bound (B&B) algorithm embedded with a constructive heuristic (CH) to obtain a tight upper bound. Since the three-stage assembly flowshop problem in PADS is strongly NP-hard, we also presented an improved tabu search (iTS) heuristic for the practical data size. Finally, we conducted a series of numerical experiments based on artificial data sets guided by characteristics obtained from practical pharmacy data sets. The computational results showed that the proposed CH algorithm is efficient, and when the computational time was allowed, the iTS algorithm could further enhance the performance. Moreover, the efficiency of collating sub-orders has a significant impact on the overall performance of PADS.