The three-dimensional nesting problem with continuous rotations
Three-dimensional nesting. Continuous rotations. Mathematical model.
Heuristics. Viewer.
The three-dimensional nesting problem (3D-NP) consists of finding the best layout for the allocation
of irregular three-dimensional pieces in a container. This problem appears in industries
that deal with production and logistics. We consider a 3D-NP where objects can be rotated by
any angle, justifying its nonlinear nature. Because it is a not well-studied version of the problem,
there are several gaps to fill related to solution methods and test instances. Our goal is to
answer the following research question: “ Is there any way to improve the efficiency of solving
the three-dimensional nesting problem with continuous rotations, either by heuristics or solving
the model using any solver?”. This project has four main goals to contribute in the literature:
(i) establish a systematic generator of test instances; (ii) propose algorithms to obtain fast and
accurate solutions; (iii) introduce a mathematical model with different approaches to deal with
overlapping of pieces; (iv) design an interactive viewer for a given solution. To date, we implemented
a test instance generator, a viewer prototype, and a constructive heuristic. For the
next steps, we explain how we will develop other algorithms, the mathematical model, and the
improvement of the viewer software’s functionalities.