Multi-phase scheduling of 3D-printed devices for medicine

3D-printed anatomical models and medical devices for medical use sup- port surgery planning, surgeons’ training, and other important activities [1,2,3]. Nowadays, outsourced companies supply 3D-printed devices to hospitals, while only a few services have been in-sourced within the hospital worldwide. However, this con- figuration will be exploited more and more in the future because it involves physicians more directly in the process, thus reducing production times and costs. Efficient additive manufacturing organizations require solving combinatorial opti- mization problems [4,5]. In particular, properly managing in-hospital 3D factories is a complex task, due to the requirements to be considered when scheduling the oper- ations. Typically, an order for a 3D-printed device involves four production phases: two pre-processing phases (segmentation of the patient-specific medical images and design of the device), the 3D printing itself, and a post-processing phase (cleaning and finishing). Furthermore, each order requires a specific set of materials on the printer and changing materials could be wasteful (expensive) and time-consuming. We developed a multi-phase scheduler suited for in-hospital 3D factories to max- imize production and minimize its cost. This scheduler considers the production of devices with different due dates, priorities, activities’ duration, and material consump- tion. Although the main purpose is the selection of orders to be executed, the same production can lead to different material consumption, depending on the assignment of orders to printers and their sequencing. To this aim, we introduce a hierarchical multiobjective integer linear programming model and a matheuristic approach able to solve the multi-phase scheduling problem for real-size instances. The effectiveness of the proposed method is demonstrated through a computational analysis using real instances from the 3D4Med Clinical 3D Printing Laboratory of IRCCS Policlinico San Matteo, Pavia, Italy.