Scheduling inspired models for two-dimensional packing problems
AbstractWe 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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Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 215 (2011)
Issue (Month): 1 (November)
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Web page: http://www.elsevier.com/locate/eor
Optimization Integer programming Strip packing Resource-Task Network Spatial grids;
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- Toledo, Franklina M.B. & Carravilla, Maria AntÃ³nia & Ribeiro, Cristina & Oliveira, JosÃ© F. & Gomes, A. Miguel, 2013. "The Dotted-Board Model: A new MIP model for nesting irregular shapes," International Journal of Production Economics, Elsevier, Elsevier, vol. 145(2), pages 478-487.
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