# Object Packing and Scheduling for Sequential 3D Printing: a Linear Arithmetic Model and a CEGAR-inspired Optimal Solver

arXiv: https://arxiv.org/abs/2503.05071 · HTML: https://mlsanity.com/paper/2503.05071/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 29 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Builds on (most cited first, 1 of 1)

- [Optimal Rectangle Packing: An Absolute Placement Approach](https://mlsanity.com/paper/1402.0557/) (2014)

## Built on by (most cited first, 1 of 1)

- [Portfolio of Solving Strategies in CEGAR-based Object Packing and Scheduling for Sequential 3D Printing](https://mlsanity.com/paper/2603.12224/) (2026)

## Abstract (arXiv)

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 using a solver for satisfiability modulo theories (SMT). However, we do not solve the formula expressing the problem of object arrangement and scheduling directly, but we have proposed a technique inspired by counterexample guided abstraction refinement (CEGAR), which turned out to be a key innovation to efficiency.