Scheduling inspired models for two-dimensional packing problems
We propose two exact algorithms for two-dimensional orthogonal packing problems whose main components are simple mixed-integer linear programming models. Based on the different forms of time representation in scheduling formulations, we extend the concept of multiple time grids into a second dimension and propose a hybrid discrete/continuous-space formulation. By relying on events to continuously locate the rectangles along the strip height, we aim to reduce the size of the resulting mathematical problem when compared to a pure discrete-space model, with hopes of achieving a better computational performance. Through the solution of a set of 29 test instances from the literature, we show that this was mostly accomplished, primarily because the associated search strategy can quickly find good feasible solutions prior to the optimum, which may be very important in real industrial environments. We also provide a comprehensive comparison to seven other conceptually different approaches that have solved the same strip packing problems.
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- Kenmochi, Mitsutoshi & Imamichi, Takashi & Nonobe, Koji & Yagiura, Mutsunori & Nagamochi, Hiroshi, 2009. "Exact algorithms for the two-dimensional strip packing problem with and without rotations," European Journal of Operational Research, Elsevier, vol. 198(1), pages 73-83, October.
- Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
- Wu, Yong & Li, Wenkai & Goh, Mark & de Souza, Robert, 2010. "Three-dimensional bin packing problem with variable bin height," European Journal of Operational Research, Elsevier, vol. 202(2), pages 347-355, April.
- Ortmann, Frank G. & Ntene, Nthabiseng & van Vuuren, Jan H., 2010. "New and improved level heuristics for the rectangular strip packing and variable-sized bin packing problems," European Journal of Operational Research, Elsevier, vol. 203(2), pages 306-315, June.
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