Three-dimensional (3D) printing has great potential for establishing a ubiquitous service in the medical industry. However, the planning, optimization, and control of a ubiquitous 3D printing network have not been sufficiently discussed. Therefore, this study established a collaborative and ubiquitous system for making dental parts using 3D printing. The collaborative and ubiquitous system split an order for the 3D printing facilities to fulfill the order collaboratively and forms a delivery plan to pick up the 3D objects. To optimize the performance of the two tasks, a mixed-integer linear programming (MILP) model and a mixed-integer quadratic programming (MIQP) model are proposed, respectively. In addition, slack information is derived and provided to each 3D printing facility so that it can determine the feasibility of resuming the same 3D printing process locally from the beginning without violating the optimality of the original printing and delivery plan. Further, more slack is gained by considering the chain effect between two successive 3D printing facilities. The effectiveness of the collaborative and ubiquitous system was validated using a regional experiment in Taichung City, Taiwan. Compared with two existing methods, the collaborative and ubiquitous 3D printing network reduced the manufacturing lead time by 45% on average. Furthermore, with the slack information, a 3D printing facility could make an independent decision about the feasibility of resuming the same 3D printing process locally from the beginning.