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

Abstract

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 Review of Mark Planning Problem

“…The basic five heuristics based on constructive concept are developed in [9]. The first four algorithms (H1-H4) are inspired from rule of thumb used by experts of the garment industry whereas the last algorithm (H5) is a random search which randomly generates a set of markers satisfying demand orders.…”

“…Each marker can be described by three dimensions, namely, length, width and height. Marker width is varied depending on a width of fabric roll used which is typically assumed to be constant in many researches [9,10]. A length of each marker is restricted to some specific upper bounds which its value depending on a planner or a cutting table length.…”

“…Furthermore, 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 [9].…”

“…The important assumption of most papers in this group is to assume that a fabric width is constant. So, minimization of fabric area used is equal to minimization of total fabric length used [9,24]. This objective function is used based on the insertion effect.…”

“…Almost papers [3,9,12,[18][19][20][21][22][23][24]26] used only a set of basic constraints addressed in the basic mark planning model as shown in section 2.2. However, in [16,17], they add a constraint that allows no excess to occur.…”