A large neighborhood search matheuristic for the two-dimensional guillotine flexible stock size cutting stock problem
Abstract
This paper introduces the two-dimensional flexible stock size cutting stock problem (2D-FSSCSP), where stocks of flexible (bounded) sizes are available. The problem consists of cutting a set of smaller rectangular items, each with given dimensions, from a set of larger rectangular plates with bounded height and width. Cutting patterns are restricted to twostage non-exact guillotine cuts and are subject to two-dimensional constraints. The objective is to minimize the total amount of used materials. The 2D-FSSCSP is first formulated using three mixed integer linear programming models: item-, strip-, and pattern-based. Different dominance properties and lower and upper bounds of the 2D-FSSCSP were considered to reduce the search space. To handle large-scale instances, a large neighborhood search (LNS) is employed. The LNS framework eliminates a few patterns and reconstructs new ones by solving subproblems such as the minimum waste pattern problem. We evaluate these approaches using newly generated instances. The numerical results enable us to analyze and evaluate the impact of different modeling strategies for managing stock-size flexibility in this variant of the 2D-CSP.
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BibTeX
@article{salem2026large,
title = {{A large neighborhood search matheuristic for the two-dimensional guillotine flexible stock size cutting stock problem}},
author = {Khadija Hadj Salem and Alexis Robbes},
journal = {European Journal of Operational Research},
year = {2026},
month = aug,
doi = {10.1016/j.ejor.2026.08.023},
url = {https://hal.science/hal-05734367v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - A large neighborhood search matheuristic for the two-dimensional guillotine flexible stock size cutting stock problem
AU - Khadija Hadj Salem
AU - Alexis Robbes
PY - 2026
DA - 2026/08/18
JO - European Journal of Operational Research
DO - 10.1016/j.ejor.2026.08.023
UR - https://hal.science/hal-05734367v1
AB - This paper introduces the two-dimensional flexible stock size cutting stock problem (2D-FSSCSP), where stocks of flexible (bounded) sizes are available. The problem consists of cutting a set of smaller rectangular items, each with given dimensions, from a set of larger rectangular plates with bounded height and width. Cutting patterns are restricted to twostage non-exact guillotine cuts and are subject to two-dimensional constraints. The objective is to minimize the total amount of used materials. The 2D-FSSCSP is first formulated using three mixed integer linear programming models: item-, strip-, and pattern-based. Different dominance properties and lower and upper bounds of the 2D-FSSCSP were considered to reduce the search space. To handle large-scale instances, a large neighborhood search (LNS) is employed. The LNS framework eliminates a few patterns and reconstructs new ones by solving subproblems such as the minimum waste pattern problem. We evaluate these approaches using newly generated instances. The numerical results enable us to analyze and evaluate the impact of different modeling strategies for managing stock-size flexibility in this variant of the 2D-CSP.
SN - 0377-2217
SN - 1872-6860
ER -