Packing Problems
Manufacturer's pallet loading problem

This problem consists on arranging
(orthogonally and without overlapping) the maximum number of identical
rectangles into a large rectangle.
E. G. Birgin, R. D. Lobato and R. Morabito, "An effective recursive
partitioning approach for the packing of identical rectangles in a rectangle",
Journal of the Operational Research Society 61, pp. 306320, 2010.
[Abstract]
[pdf]
[ps]
[Website and code]
E. G. Birgin, R. Morabito and F. H. Nishihara "A note on an Lapproach for
solving the manufacturer's pallet loading problem", Journal of the
Operational Research Society 56, pp. 14481451, 2005.
[Abstract]
[pdf]
[ps]
R. Andrade and E. G. Birgin, "Symmetrybreaking constraints for packing
identical orthogonal rectangles within polyhedra", Optimization Letters 7,
pp. 375405, 2013. [Abstract]
[pdf]
Distributor's pallet loading problem

This problem consists of cutting different types of
rectangular pieces from a rectangular plate.
E. G. Birgin, R. D. Lobato and R. Morabito, "Generating unconstrained
twodimensional nonguillotine cutting patterns by a recursive
partitioning algorithm", submitted, 2010.
[Abstract]
[pdf]
[Website]

MIP models considering leftovers:
R. Andrade, E. G. Birgin, and R. Morabito, "Twostage twodimensional
guillotine cutting stock problems with usable leftovers", International
Transactions in Operational Research, to appear (DOI: 10.1111/itor.12077). [Abstract]
[pdf]
R. Andrade, E. G. Birgin, R. Morabito, and D. P. Ronconi, "MIP models for
twodimensional nonguillotine cutting problems with usable leftovers",
Journal of the Operational Research Society, to appear (DOI:
10.1057/jors.2013.108). [Abstract]
[pdf]
Packing circles and spheres by Nonlinear Optimization
We considered several packing problems using nonlinear programming
models:

Minimizing the object dimensions in circle and sphere packing problems:
E. G. Birgin and F. N. C. Sobral, "Minimizing the object dimensions in
circle and sphere packing problems", Computers & Operations
Research 35, pp. 23572375, 2008.
[Abstract]
[pdf]
[ps]
[Website and code]
E. G. Birgin and J. M. Gentil, "New and improved results for packing
identical unitary radius circles within triangles, rectangles and strips",
Computers & Operations Research 37, pp. 13181327, 2010.
[Abstract]
[pdf] [Website and code]

Packing the maximum number of identical
circles within circular and rectangular regions:
E. G. Birgin, J. M. Martínez and D. P. Ronconi, "Optimizing the Packing of
Cylinders into a Rectangular Container: A Nonlinear Approach", European
Journal of Operational Research 160, pp. 1933, 2005.
[Abstract]
[pdf]
[ps]
[Code]

Packing the maximum number of identical
circles within ellipses:
E. G. Birgin, L. H. Bustamante, H. F. Callisaya, and J. M. Martínez, "Packing circles within ellipses", International Transactions in Operational Research 20, pp. 365389, 2013.
[Abstract]
[pdf]
[Code]
Packing rectangles within arbitrary convex regions by Nonlinear Optimization
We considered several packing problems using nonlinear programming
models:

Packing of the maximum number of rectangular
items within arbitrary convex regions:
E. G. Birgin and R. D. Lobato, "Orthogonal packing of identical rectangles
within isotropic convex regions", Computers & Industrial Engineering 59, pp. 595602, 2010.
[Abstract]
[pdf]
[Code]
E. G. Birgin, J. M. Martínez, F. H. Nishihara and D. P. Ronconi,
"Orthogonal packing of rectangular items within arbitrary convex regions by
nonlinear optimization", Computers & Operations Research 33, pp.
35353548, 2006.
[Abstract]
[pdf]
[ps]
[Code]

Packing of the maximum number of freerotated
rectangular (and arbitrary polygonal) items within arbitrary convex
regions:
E. G.Birgin, J. M. Martínez, W. F. Mascarenhas and
D. P. Ronconi "Method of Sentinels for Packing Items whitin Arbitrary
Convex Regions", Journal of the Operational Research Society
57, pp. 735746, 2006.
[Abstract]
[pdf]
[ps].
W. F. Mascarenhas and E. G. Birgin, "Using sentinels to detect intersections of convex and nonconvex polygons", Computational & Applied Mathematics 29, pp. 247267, 2010.
[Abstract]
[pdf]
[ps]
