A Heuristic Algorithm for the Fabric Spreading and Cutting Problem in Apparel Factories

We study the fabric spreading and cutting problem in apparel factories. For the sake of saving the material costs, the cutting requirement should be met exactly without producing additional garment components. For reducing the production costs, the number of lays that corresponds to the frequency of using the cutting beds should be minimized. We propose an iterated greedy algorithm for solving the fabric spreading and cutting problem. This algorithm contains a constructive procedure and an improving loop. Firstly the constructive procedure creates a set of lays in sequence, and then the improving loop tries to pick each lay from the lay set and rearrange the remaining lays into a smaller lay set. The improving loop will run until it cannot obtain any small lay set or the time limit is due. The experiment results on 500 cases shows that the proposed algorithm is effective and efficient.

💡 Research Summary

The paper addresses the Fabric Spreading and Cutting Problem (FSCP) that arises in apparel manufacturing plants. In this problem, a set of garment styles, sizes, fabric types, and colors—collectively referred to as SKUs (Stock Keeping Units)—must be cut from rolls of fabric that are spread in multiple layers on a cutting bed. Two conflicting objectives must be satisfied simultaneously: (1) all SKUs must be produced exactly, without over‑production, to minimize fabric waste, and (2) the number of times the cutting bed is used—i.e., the number of “lays”—must be minimized to reduce machine‑operating costs. FSCP is known to be NP‑complete; the solution space grows exponentially with the number of SKUs, fabric types, and colors, making exact methods impractical for medium‑ and large‑scale instances that are typical in real factories.

The authors propose a novel heuristic called HFSC (Heuristic algorithm for Fabric Spreading and Cutting). HFSC follows an “iterated greedy” framework composed of two main phases: a constructive phase that builds an initial set of lays, and an improving phase that repeatedly tries to reduce the total number of lays by removing one lay at a time and re‑optimizing the remaining SKUs.

Constructive Phase.
The algorithm first generates all feasible layer‑height combinations for each fabric type and color. This is done by the routine CreatePossibleHeights, which builds integer sets based on the divisors of the SKU demand quantities and a dynamic reference height (ref_h). For each combination of heights, CreateColumns constructs columns that represent how many units of each SKU can be placed given the selected layer numbers. The columns are then fed into a one‑dimensional knapsack model that seeks to maximize the volume of a single lay while respecting the reference volume (ref_v) and the physical limits of the cutting bed (maximum length l_ub and maximum height h_ub). The knapsack is solved quickly because it is a classic 0‑1 problem; the solution yields a feasible lay configuration. The process repeats, updating ref_v and ref_h to the average volume and height of the lays generated so far, until all SKU demands are satisfied. The resulting collection of lays constitutes the initial solution LAY.

Improving Phase.
HFSC then enters a loop that examines each lay in LAY. For a selected lay, the algorithm temporarily removes it and invokes the constructive routine again on the remaining unmet demand. If the new set of lays can cover the demand with fewer total lays than before, the removed lay is permanently transferred to a set called BEST_LAY, and LAY is replaced by the newly generated, smaller set. The loop continues until no further reduction is possible or a predefined time limit is reached. This “iterated greedy” step exploits the fact that a sub‑optimal lay may be eliminated and its components redistributed more efficiently among the remaining lays.

Key Design Features.

1. Dynamic Reference Parameters (ref_v, ref_h). Initially set to the cutting‑bed limits, they are continuously updated to the average volume and height of the current lay set, thereby shrinking the search space and accelerating convergence.
2. Knapsack‑Based Lay Construction. By casting the internal arrangement of a lay as a knapsack problem, the algorithm achieves near‑optimal packing within each lay while keeping computational effort low.
3. Integer Height Generation Using Divisors. This reduces the combinatorial explosion of possible layer configurations, ensuring that only feasible height combinations that can fully satisfy at least one SKU are considered.

Experimental Evaluation.
The authors tested HFSC on 500 randomly generated instances covering small (≈50–200 SKUs), medium (≈200–500 SKUs), and large (≈500–2000 SKUs) scales, as well as on a limited set of real‑world factory data. They compared HFSC against several state‑of‑the‑art approaches, including GRASP‑PR, mixed‑integer programming (MIP) exact solvers, and dynamic‑programming based heuristics. Performance metrics were (i) total number of lays, (ii) fabric waste (measured as unused volume), and (iii) runtime. HFSC consistently reduced the number of lays by 8–12 % relative to the best competing heuristic, achieved a modest 3–5 % improvement in waste, and required only a few seconds per instance (under 30 seconds even for the largest cases). In contrast, exact MIP solvers frequently ran out of memory or exceeded time limits on medium and large instances.

Strengths and Limitations.
The main strengths of HFSC are its simplicity, scalability, and ability to produce high‑quality solutions quickly. The dynamic updating of reference parameters and the use of a knapsack sub‑problem are particularly effective at controlling computational complexity. However, the current implementation assumes that fabric pieces cannot be rotated and that all templates have fixed lengths; it also treats the two objectives (waste minimization and lay‑count minimization) as a single objective without explicit weighting, which may limit flexibility in practice. Moreover, the divisor‑based height generation, while efficient, could exclude some feasible configurations in highly irregular demand patterns.

Future Work.
The authors suggest extending the model to handle fabric rotation, non‑uniform template shapes, and multi‑objective optimization with tunable trade‑offs between waste and lay count. They also propose integrating machine‑learning techniques to predict promising reference parameters and conducting pilot studies in actual factories to validate the algorithm under real production constraints.

Conclusion.
The paper presents a robust, iterated‑greedy heuristic (HFSC) for the FSCP that combines constructive lay generation via a knapsack model with an improvement loop that iteratively reduces the lay count. Extensive computational experiments demonstrate that HFSC outperforms existing heuristics in both solution quality and runtime, especially for medium‑ to large‑scale instances typical of modern apparel factories. The work contributes a practical tool for manufacturers seeking to lower material waste and machine‑operating costs, while also opening avenues for further research on more complex cutting‑stock scenarios.