用平面运输系统优化个性化药物生产全流程，提升效率与可扩展性。
Integrated packing, placement, scheduling, and routing of personalized production: a pharmaceutical Industry 4.0 use-case with a planar transport system
- 基于历史处方数据优化药品布局，减少搬运距离。
- 混合整数二次规划与约束编程结合，实现高效调度与路径规划。
- 适合制药业智能制造场景，支持每日数百订单的实时处理。
平面运输系统的兴起要求重新评估柔性制造系统（FMS），以同时优化内部物流与生产调度。该系统在基于瓦片的平面网格上运行，使移动单元具备二维自由度，克服了传统串行产线的效率瓶颈。本文将平面FMS框架应用于医药行业真实案例：个性化药物自动化生产。该系统需在战术与操作两个层面解决优化问题。战术层涉及生产线布局与药剂分配器定位，采用混合整数二次规划模型解决包装问题，利用历史患者数据中的药品共现模式；随后通过双层优化求解布局问题，结合分配问题与带邻域的最短哈密顿路径，最小化预期搬运距离。操作层每日执行，需快速调度移动单元处理新订单。该调度问题采用约束编程建模，将移动单元视为资源池以保障订单完整性，并通过迭代冲突消解机制与基于有向无环图（DAG）的推理，生成无冲突路径。基于40种药物的真实处方数据评估表明，该框架在多种布局拓扑下可高效扩展至500个订单，调度结果高效且计算可行，适用于日常运营。
原文摘要 · Abstract (English)
The recent emergence of planar transport systems necessitates re-evaluation of Flexible Manufacturing Systems (FMS) to address the simultaneous scheduling of internal logistics and production operations. By operating on a tile-based planar grid, these systems allow independent movers full two-dimensional freedom, mitigating inefficiencies inherent to traditional sequential lines. This paper applies a planar FMS framework to a real-world use case in the pharmaceutical industry: the automated production of personalized drugs. Implementing this system requires solving optimization problems at both tactical and operational levels. The tactical level involves decisions regarding production line layout and the positioning of drug dispensers. A Mixed-Integer Quadratic Programming model is utilized for the packing problem to exploit drug co-occurrence patterns found in historical patient data. Subsequently, we solve the placement problem - a bi-level problem combining an assignment problem with Shortest Hamiltonian paths with neighborhoods - to arrange dispensers in a layout minimizing expected travel distances. The operational level is encountered daily, scheduling individual movers to process new orders as quickly as possible. This scheduling problem is formulated using Constraint Programming, modeling movers as reservoir resources to ensure order completeness, complemented by a routing phase using an iterative conflict-resolution mechanism and DAG-based reasoning to convert schedules into conflict-free paths. Evaluation using real-world prescription data for 40 drugs shows the framework scales efficiently across several layout topologies for up to 500 orders, with schedules that are highly effective and computationally tractable for daily operations.
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