The article examines a hybrid approach for optimizing one-dimensional stock cutting. The proposed approach combines two methods: the
pattern-oriented LP-based method, and the
item-oriented sequential ...heuristic procedure. The purpose of such a combined method is its ability to cut order lengths in exactly required number of pieces and to cumulate consecutive residual lengths in one piece which could be used later. The sample problem is presented and solved.
The article examines the Sequential Heuristic Procedure (SHP) for optimising one-dimensional stock cutting when all stock lengths are different. In order to solve a bicriterial multidimensional ...knapsack problem with side constraints a lexicographic approach is applied. An
item-oriented solution was found through a combination of approximations and heuristics that minimize the influence of
ending conditions leading to almost optimal solutions. The computer program CUT was developed, based on the proposed algorithm. Two sample problems are presented and solved. A statistical analysis of parameters that affect material utilisation was also made.
The paper deals with the problem of evaluating and comparing different one-dimensional stock cutting algorithms regarding trim loss. Different types of problems are identified. An evaluation method ...is developed which enables a comparison of solutions of all types of problems. A practical example of this methods implementation is presented.
There are many algorithms and methods for one-dimensional stock cutting with different factors that need to be taken into account. Therefore a general comparison between them is very difficult if not impossible. However, if we assume that trim loss is the most important factor common to different methods, we can overcome this problem by limiting the comparison to trim loss. In different cutting stock problems and in different approaches to them trim loss is defined differently. For the comparison of different solutions to be possible, we need to find a common definition to the trim loss. Such a general definition is introduced by the General One-Dimensional Cutting Stock Problem type (G1D-CSP). In this paper, a problem generator algorithm
PGEN for G1D-CSP is presented and the method for evaluation and comparison of different one-dimensional cutting stock algorithms is proposed.
The article examines the sequential heuristic procedure for optimisation of roll cutting in the clothing industry. The issue of roll cutting can be defined as a bicriterial multidimensional knapsack ...problem with side constraints. To handle the bicriterial objective function a lexicographic approach is proposed. An item-oriented solution was found through a combination of approximations and heuristics. A sample problem is presented and solved.
