Exact and heuristic algorithms for the circle cutting problem in the manufacturing industry of electric motors

Circular blanks are often cut from silicon steel plates to make stators and rotors of electric motors. The shearing and punching processes are often used to cut the blanks. First a guillotine shear cuts the plate into strips, and then a stamping press cuts the blanks from the strips. The unconstrained circle cutting problem discussed is the problem of cutting from a rectangular plate a number of circular blanks of given diameters and values, so as to maximize the value of blanks cut, where the shearing and punching processes are applied. Two algorithms based on dynamic programming are presented for generating cutting patterns, one is an exact algorithm and the other is a heuristic one. The computational results indicate that the exact algorithm is adequate for small and middle scale problems, the heuristic algorithm is much more time efficient, and can generate cutting patterns close to optimal.