Packing boxes with harmonic bricks

Online strip packing with modifiable boxes

Fast Truck - Packing of 3 D boxes

The purpose of this research is to estimate the repair effects a repairable system undergoes repeated failures and repairs. Data was collected on a cement kiln incurring150 failures and 5 shutdowns for overhaul. Causes of failure were identified as operational, mechanical or electrical. The unit was restarted but with an (expected) improved failure rate by virtue of the repair. Repair improveme...

Packing ellipsoids into volume-minimizing rectangular boxes

A set of tri-axial ellipsoids, with given semi-axes, is to be packed into a rectangular box; its widths, lengths and height are subject to lower and upper bounds. We want to minimize the volume of this box and seek an overlap-free placement of the ellipsoids which can take any orientation. We present closed non-convex NLP formulations for this ellipsoid packing problem based on purely algebraic...

Building Bricks with Bricks, with Mathematica

In this work we solve a special case of the problem of building an n-dimensional parallelepiped using a given set of n-dimensional parallelepipeds. Consider the identity x = xHx 1L Hx 2L + 3 xHx 1L + x. For sufficiently large x, we associate with x3 a cube with edges of size x, with x Hx 1L Hx 2L a parallelepiped with edges x, x 1, x 2, with 3 x Hx 1L three parallelepipeds of edges x, x 1, 1, a...

A Creative Improvisational Companion Based on Idiomatic Harmonic Bricks

We describe an improvisational companion based on the concept of harmonic bricks, as articulated by Cork and others. Our companion is software that can play background for, and trade melodies with, a human soloist. While exhibiting creativity itself, its greater purpose is to improve creativity of its user. Bricks, originally intended for memorization of chord progressions, are used here as a s...