Fig 1.
Optimal configuration for an instance from [4] with two bins and more than 50 items.
Fig 2.
The two-step methodology to solve the 2D-BPP.
Fig 3.
First step of the P&C methodology.
Fig 4.
The P&C methodology computes the points required for each item considering the grid inside of the bin.
Fig 5.
Set of valid positions when the 90° rotations are not allowed.
Table 1.
Correspondence matrix C for items of Fig 5.
Fig 6.
The new set of valid positions when rotations by 90° are allowed.
Table 2.
Benchmark instances for the 2D-BPP.
Table 3.
Execution time for the Positions stage of P&C, Algorithm 1, for the instances in Classes 1–3 of bwmv with and without rotations.
Table 4.
Execution time for the Positions stage of P&C, Algorithm 1, for the cgcut, ngcut, and beng instances with and without rotations.
Table 5.
Experimental results for Class 1 of the bwmv instances without rotations, applying the different families of valid inequalities to the set-covering ILP.
Table 6.
Experimental results for Class 2 of the bwmv instances without rotations, applying the different families of valid inequalities to the set-covering ILP.
Table 7.
Experimental results for Class 3 of the bwmv instances without rotations with n = 20 and n = 40, applying the different families of valid inequalities to the set-covering ILP.
Table 8.
Experimental results for cgcut, ngcut, and beng instances without rotations.
Table 9.
Comparative approaches for the 2D-BPP.
Table 10.
Comparison of the solutions obtained by the different approaches for the bwmv instances without rotations.
Table 11.
Comparison of the solutions obtained by the different approaches for the cgcut, ngcut, and beng instances without rotations.
Table 12.
Comparison of the solutions obtained by the different approaches for the bwmv instances when 90° rotation of the items is allowed.
Table 13.
Comparison of the solutions obtained by the different approaches for the cgcut, ngcut, and beng instances when 90° rotation of the items is allowed.