Abstract. We consider the packing problem for convex polytopes in a cuboid of minimum volume. To describe analytically the non-overlapping constraints for convex polytopes that allow continuous translations and rotations, we use phi-functions and quasi-phi-functions. We provide an exact mathematical model in the form of an NLP-problem and analyze its characteristics. Based on the general solution strategy, we propose two approaches that take into account peculiarities of phi-functions and quasi-phi-functions. Computational results to compare the efficiency of our approaches are given with respect to both the value of the objective function and runtime.

Keywords: packing, convex polytopes, phi-function, quasi-phi-function, mathematical model, nonlinear optimization.