Local Search Algorithms for the Two-Dimensional Cutting Stock Problem with a Given Number of Different Patterns

We consider the two-dimensional cutting stock problem that arises in many applications in industries. In recent industrial applications, it is argued that the setup cost for changing patterns becomes more dominant and it is impractical to use many different cutting patterns. Therefore, we consider the pattern restricted two-dimensional cutting stock problem, in which the total number of applications of cutting patterns is minimized while the number of different cutting patterns is given as a parameter n. For this problem, we develop local search algorithms. As the neighborhood size plays a crucial role in determining the efficiency of local search, we propose to use linear programming techniques for the purpose of restricting the number of solutions in the neighborhood. In this process, to generate a cutting pattern, it is required to place all the given products (rectangles) into the stock sheet (two-dimensional area) without mutual overlap. For this purpose, we develop a heuristic algorithm using an existing rectangle packing algorithm with the sequence pair coding scheme. Finally, we generate random test instances of this problem and conduct computational experiments, to evaluate the effectiveness of the proposed algorithms.