Heuristics for the combined cut order planning two-dimensional layout problem in the apparel industry

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.