Heuristics for Two-Dimensional Rectangular Guillotine Cutting Stock

Abstract

Two-Dimensional Rectangular Guillotine Cutting Stock Problem (2DRGCSP) is one of the most significant problems in the manufacturing industries. A set of small rectangular size of paper, aluminum rolls, glasses, fiber glasses, or plastic are required to cut from a set of big size rectangular sheet of its raw materials.  A guillotine cut is used, where the sheet is cut from one side to another side without changing the direction of the blade to produce the strips. Then each strip is cut again to produce the small rectangular size of panels that match with the required size, and the number of the panels must satisfy with the demand. This paper presents the heuristic techniques to solve the cutting problems. The heuristic techniques create the good cutting patterns such that the waste of the sheets is minimized and demands for each panel are satisfied. There are five proposed heuristics, developed to solve this problem. They are 2D simple heuristic cutting (2DSHC), 2D horizontal construction (2DHC), 2D vertical construction (2DVC), 2D horizontal improvement (2DHI), and 2D vertical improvement (2DVI). The testing instances are created from the real problems in the Printed Circuit Board (PCB) Company. The results are presented and compared with column generation (CG) method. The proposed heuristics provide good cutting patterns with a comparable waste to the column generation method. Moreover, the heuristics can produce solutions in a short computational time even in the large size instances, where the column generation method cannot find the solution. Therefore, these proposed heuristics techniques are applicable to solve the 2DRGCSP in the industry where the solutions from the exact algorithms cannot be found.