A Hybrid Methodology Using Heuristic Methods for Two-Dimensional Cutting and Packing Problem with Rectangular Pieces

The cutting and packing problem is the process of cutting small pieces of certain sizes and proportions from materials used for different purposes in industries. Because this problem cannot be expressed by mathematical models, combinational optimization in multidimensional space is utilized for the solution. The aim of this problem is to increase the usability of the material used for the placement process and to minimize the trim loss. In this study, a solution is presented to two-dimensional regular cutting and packing problem by a combined method consisting of improved bottom-left, bottom-left fill placement algorithms, no-fit polygon and first fit decreasing heuristic algorithms. The improved bottom-left placement algorithm for the placement of parts starting from the bottom-left part according to a certain permutation order, bottom-left fill algorithm for the placement of suitable pieces to the available free spaces in placement model, no-fit polygon method for preventing the geometric overlap between the parts and the first fit decreasing heuristic algorithm is used as the selection algorithm after ordering from large to small according to the parts areas. Placement process and performance evaluation was performed for 11 different test data. As a result of the studies carried out with combined heuristic methods, it is seen that there is a placement without any waste in P2 and P10 placement models. This shows that the optimal solution is obtained. In other placement models, a trim loss was obtained between 4.54% and 16.7%. The experimental results show the effectiveness of the proposed heuristic methods for the solution of the cutting and packing problem