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Cut order planning (COP) is an NP-hard nonlinear optimization problem. Managers of apparel manufacturing units face this problem during the planning of the first stage of the manufacturing process. It affects the fluidity of the work flow and use of fabric. It consists in dividing every garment's order into sections, assigning the sizes to them, and determining their lengths and numbers of layers such that the total fabric length is minimized. Current industrial practice assumes that the length of the layout of a section is known a priori, and it does not depend on its combination of sizes. That is, the industry solves COP independently of the two-dimensional layout (TDL) that is the second stage of the manufacturing process. By relying on the length estimates in lieu of determining the actual length of a section, the industry is obtaining erroneous estimates of the true length used. Herein, COP and TDL are combined into a single problem CT (CT = COP + TDL) whose objective is to minimize fabric length. CT is solved using constructive heuristics, and three metaheuristics: a stochastic local improvement method, global improvement method, and hybrid approach. The approaches are tested on existing benchmark instances and new industrial cases. Their results provide computational proof of the benefits that industry can ripe by combining COP and TDL. The comparison of the performance of the approaches highlights their respective academic and practical utilities.

The two-dimensional layout (TDL) optimization problem consists of finding the minimal length layout of a set of both regular and irregular two-dimensional shapes on a stock sheet of finite width but infinite length. The layout should not contain any overlap. In this paper, we solve the TDL problem by proposing two approximate algorithms. The first one is a new heuristic based on a constructive approach specifically designed for irregular shapes, but that works well with regular ones. The second is a hybrid method in which the constructive approach displays the layouts corresponding to the chromosomes yielded by the genetic algorithm. The resulting algorithm yields satisfactory results in relatively short computational times as shown by the extensive computational testing on problems from the literature.