On decomposing 3D packing problems in wooden furniture industry

This paper discusses the development of a cutting plan for three-dimensional wooden raw material pieces. Practical requirements, particularly those in wooden furniture industry, are addressed. Such considerations include the use of leftover raw material pieces and parts' color requirements. Similar parts are packed over the cross sectional area of raw material pieces first. Then the packing pattern along the length of raw material piece is considered. The material utilization criteria is used to screen out inefficient cutting patterns. In order to handle large problem sizes, the problem is decomposed into smaller lists of raw material available and parts required. Such approach not only makes the solution obtainable in reasonable time but also greatly reduces the problem size considered. A case study is used to illustrate the performance of the system developed. The program is currently used by a company that manufactures wooden picture frame. It has performed reasonably well in practice, especially in using leftover raw material pieces efficiently.