A successive elimination method for one-dimensional stock cutting problems in ship production

Abstract

One-dimensional stock cutting problems can be encountered at the production stage of many areas of engineering as well as in shipbuilding and coastal structures. In this paper, a novel approach is proposed to solve the problem directly by using the cutting patterns obtained by the analytical methods at the mathematical modeling stage. By minimizing both the number of different cutting patterns and material waste, the proposed method is able to capture the ideal solution of the analytical methods. The main advantage of the method comes from the fact that an integer solution is guaranteed. However, in analytical methods it is not always possible to produce integer solutions and the linear programming algorithm must be run repeatedly to select integer solutions from the alternatives to get practical results. The proposed nesting algorithm is a low-cost and efficient tool. Minimizing the number of cutting patterns contributes to time and material savings. Also, by using this method trim loss is minimized and stock usage is maximized. The efficiency of the proposed method is demonstrated by extensive numerical results.