Search

This paper studies a two-dimensional two-stage guillotine cutting stock problem which includes determination of how the items should be cut from stock panels in an optimal way, by developing and applying different solution approaches. An integer programming model with new features is proposed. A random key based genetic algorithm is utilized to obtain feasible solutions, and by applying a local search within the algorithm, a hybrid structure is acquired. Besides, a novel two-stage math-heuristic solution method is proposed. In the first stage of this method, a relaxation of the problem is solved; in the second, this solution is improved. The time to obtain the results of the developed two-stage math-heuristic solution approach is significantly lower than the other methods given in the article. Optimal solution values were obtained in 26 of 30 test problems taken from the literature with the proposed mathematical model, in 14 with mathematical programming based heuristic method, and in 16 with a random key based genetic algorithm. [ABSTRACT FROM AUTHOR]

Two-dimensional bin packing problem (2DBPP) is a sub-branch of cutting and packaging problems (CPP). Researchers often use meta-heuristic algorithms in the solution of 2DBPP, because in cases where a large number of samples exist, meta-heuristic algorithms reach acceptable solutions in reasonable time. In this article, a novel hybrid meta-heuristic algorithm is proposed for the solution of 2DBPP. The proposed algorithm combines flower pollination algorithm (FPA) and genetic algorithm (GA). In order to improve FPA's global search capability, FPA's local search operator is modified. The proposed algorithm has been compared to six recently published meta-heuristic algorithms. For comparison, a data set containing 10 classes, 50 subgroups and 500 samples was used. Average container values of each class and of each subgroup were used as comparison parameters. In addition, Friedman test was used to evaluate the relative performance of the algorithms. The proposed algorithm achieved the most successful results in 6 of the 10 classes of the data set and 33 of the 50 subgroups. In the Friedman test, it was the most successful algorithm with a score of 2.6. The results confirm the validity of the proposed meta-heuristic algorithm. [ABSTRACT FROM AUTHOR]

In solving cutting stock problems, generally, cutting patterns are generated first, and then it is determined which cutting plans will be used. On the other hand, the difficulty of generating all cutting patterns and often the large number of cutting patterns are the main problems encountered in this regard. In this study an integrated mathematical model that generates cutting patterns and finds the best patterns is developed for 1.5-dimensional cutting stock problems with order type and strip number constraints. This non-linear model has been linearized to eliminate solution difficulties. The performance of both models is compared with the performance of the model that uses the previously generated cutting patterns by using the randomly generated test problems. Obtained results show that the linear model, which also generates the cutting patterns itself, can be solved in a reasonable time up to a certain size. In particular, we believe that linearization of the nonlinear mathematical model for the problem will be an important contribution for the literature. [ABSTRACT FROM AUTHOR]

Cutting stock problems is one of the most encountered problems in production and planning. In this work, an One-Dimensional Cutting Stock Problem which is encountered in companies which are in steel industry is discussed. The companies desires both minimization of the trim loss in cutting patterns and changes of the cutters in cutting process when preparing customer orders. In this work, a new heuristic algorithm for the encountered integrated problem. Finally, the efficiency of the proposed algorithm on real-life problems is showed. [ABSTRACT FROM AUTHOR]