Cardiff Mathematics Reader Dr Rhyd Lewis paves the way for more sustainable industry

‘More haste towards less waste’ has been one of the loudest calls for sustainable business practices in recent years, as we all look to reduce our individual carbon footprint and, more widely, to reduce heavy industry’s impact on the planet.

As inflation has increased in recent times, our industries also need to make savings on cost and materials, so how does manufacturing achieve those aims in a way that’s beneficial to both the bottom line and the planet?

Reader in Mathematics at Cardiff University Dr Rhyd Lewis has provided a solution in his publication ‘How to Pack Trapezoids: Exact and Evolutionary Algorithms’, co-written with Dr Penny Holborn (University of South Wales). In this paper, he shows how ideas taken from the mathematical field of graph theory can be used to design algorithms that can optimally pack trapezoidal items so that inter-item waste is minimised.

Already, these new algorithms have been applied by the Fraunhofer Institute for Algorithms and Scientific Computing SCAI into brand new software AutoBarSizer, which generates optimised layouts for cutting materials, notably steel profiles (metal beams), as well as other bars and rods.

The generated layouts achieve an extremely high degree of material utilization (yield) and reduce cutting waste, thereby reducing physical waste by manufacturers on unnecessary materials. AutoBarSizer can potentially reduce financial waste on costs for business by both reducing stock waste and costly disposal by encouraging more efficient use of reusable remnants, thus protecting profitability.

Further potential benefits can occur where software like AutoBarSizer could be applied to scarce or finite materials, either now or in the future, by ensuring that materials are fully used and not contributing to additional scarcity.

A representative for The Fraunhofer Institute for Algorithms and Scientific Computing SCAI, Onno Garms, outlined that The Fraunhofer Institute “combines know-how in mathematical and computational methods with a focus on the development of innovative algorithms and their take-up in industrial practice... Our institute has developed the AutoBarSizer software to solve this optimization problem by combining the algorithms designed and published by Dr Lewis with our own research. As an active research organization ourselves, we are always very happy to see new techniques such as these finding their way into industrial practice.”

Dr Rhyd Lewis is a Reader in Mathematics at Cardiff University, with further publications on school bus routing, medical theatre/sports scheduling, as well as algorithmic graph theory and graph colouring.

This innovative consideration by Dr Rhyd Lewis of the trapezoid packing problem is yet another example of how Cardiff mathematicians are making swift strides in addressing crucial challenges facing industry today, providing tangible solutions to benefit us all as global citizens.