A Linear Arithmetic Model Reflecting Vertical Object Details in Object Packing and Scheduling for Sequential 3D Printing

We address the problem of object arrangement and scheduling for sequential 3D printing. Unlike the standard 3D printing, where all objects are printed slice by slice at once, in sequential 3D printing, objects are completed one after other. In the sequential case, it is necessary to ensure that the moving parts of the printer do not collide with previously printed objects. We look at the sequential printing problem from the perspective of combinatorial optimization. We propose to express the problem as a linear arithmetic formula, which is then solved by a solver for satisfiability modulo theories (SMT). The formula is designed to take vertical details of objects into account. To solve the model we propose a technique inspired by counterexample guided abstraction refinement (CEGAR), which turned out to be a key innovation to efficiency.