A bi-objective guillotine cutting problem of stamping strips of equal circles

Abstract

Some factories use the cutting and stamping processes to divide stock plates into circles to make products. A guillotine machine cuts the plate into strips in the cutting process and then a stamping press punches out circles from the strips in the stamping process. The circles in a strip have the same size. The number of rows of circles in each strip is limited. Under these constraints, this paper addresses the following primary objective: to cut a plate by a guillotine method so that the maximal number of circles is obtained. Then the secondary objective should be optimized: the cutting layout should use a minimal number of strips. The problem is formulated as a bi-objective optimization problem and a recursive algorithm is presented for it. The computational results indicate that the algorithm can efficiently simplify the cutting process.

Keywords:

• recursive algorithm
• two-dimensional cutting
• circle packing
• stamping strips

2000 AMS Subject Classifications :

• 90C27
• 05B40
• 90C90
• 11H31
• 52C15
• 52C17

Acknowledgements

This research is supported in part by the National Natural Science Foundation Project (60763011) and Guangxi Science Foundation Project (0728100).