Selecting the best sheet length for the steel stock used in circular blank production

Silicon steel circular blanks are often used in the manufacture of electric motors. Most factories use rectangular sheets to make these blanks, however, the silicon steel is usually produced in rolls and thus these rolls must be cut at the steelworks into sheets with user-specified lengths. An algorithm to determine the optimal sheet length is presented in this paper. It considers the sheet lengths in an ascending order, and selects the best one of them. The optimal solution for a specific length is then taken to be the initial solution of the next length. A cutting pattern usually consists of one or two segments. Strips in a segment have the same length and direction, which is either horizontal or vertical. More than one row of identical blanks can be produced from a strip. The algorithm uses dynamic programming to determine the optimal strip layouts on segments, and finds the optimal segment lengths through implicit enumeration. The computational results indicate that the algorithm is efficient both in computation time and in material usage. Finally, the solution to an example is presented.