Academic Journal
Mixed-integer linear programming models for 3D irregular strip packing problems.
| Τίτλος: | Mixed-integer linear programming models for 3D irregular strip packing problems. |
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| Συγγραφείς: | Tollenaere, Jonas1 (AUTHOR) jonas.tollenaere@kuleuven.be, Martinez-Sykora, Antonio2 (AUTHOR), Wauters, Tony1 (AUTHOR) |
| Πηγή: | European Journal of Operational Research. Jun2026, Vol. 331 Issue 2, p365-380. 16p. |
| Θεματικοί όροι: | *Packing problem (Mathematics), *Mathematical programming, Mixed integer linear programming, Benchmark problems (Computer science), Constraint satisfaction, Convex bodies |
| Περίληψη: | • We observe a lack of exact methods in the 3D irregular cutting and packing literature in comparison to the 2D literature. • An exact approach for solving 3D irregular strip packing problems is proposed to address this deficit. • Our approach concerns a mixed-integer linear programming model based on No-Fit Polyhedra. • Established strengthening techniques from the 2D literature are adapted to 3D. • An extended series of benchmarks is introduced to thoroughly benchmark this approach. Exact solution methods for two-dimensional irregular strip-packing problems have been studied and refined over the years. In contrast, the three-dimensional version of the problem has only been addressed through heuristic solution methods or approximating representations, resulting in a lack of optimal solutions. This paper addresses this gap in the literature by formulating and solving exact models of three-dimensional irregular strip packing problems. When taking these foundational first steps, we will focus on instances with convex items and not consider rotation of the items. The most challenging aspect when modelling such problems is the formulation of separation constraints that ensure that none of the items overlap. Many of the exact models introduced for two-dimensional problems tackle this challenge using No-Fit Polygons, which describe the relative placements for which two items overlap. For our three-dimensional case, we introduce a mixed integer linear programming formulation based on their conceptual equivalents: No-Fit Polyhedra. A basic first model can be formulated in a relatively straightforward manner, but it exhibits weak linear relaxations and a high degree of symmetry. Therefore, we investigate whether the techniques used to strengthen two-dimensional formulations can also be adapted for our three-dimensional context. An extensive set of instances is introduced to thoroughly benchmark the impact of these techniques and to evaluate their overall performance. [ABSTRACT FROM AUTHOR] |
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