Calculus of packaging optimisation: The pyramid box

The calculus of optimisation is not new to packaging problems. The first publication on this topic is attributed to Todhunter who published his open-top box problem in 1855. The volume maximisation of open-top boxes is no longer the answer to the problems facing the rapidly changing industrial world that we live in. In today’s profit-driven packaging industry, packaging optimisation is one important component of the supply chain from production to automotive high-tech assembly that no environmental agency can afford to overlook or underestimate. Even a square centimetre reduction in materials used in packaging can translate into massive cost savings, reducing tons of packaging waste and easing the burden on landfill sites. It is the aim of this article to use the calculus of optimisation coupled with geometry and trigonometry to provide some important cost and waste reduction information for the packaging industry. The techniques used are simple, but the approach and the results are eye-opening and interesting.