Simplest optimal guillotine cutting patterns for strips of identical circles

The manufacturing industry often uses the cutting and stamping process to divide stock plates into circles. A guillotine machine cuts the plate into strips for stamping at the cutting stage, and then a stamping press punches out the circles from the strips at the stamping stage. The problem discussed is to cut a plate into strips of identical circles such that the number of circles is maximized. A dynamic programming algorithm is presented for generating the simplest optimal cutting patterns of the strips. The computational results indicate that the algorithm is very efficient in simplifying the cutting process.