This paper is the second of a two part series and describes new lower and upper bounds for a more general version of the Two-Dimensional Finite Bin Packing Problem (2BP) than the one considered in Part I (see Boschetti and Mingozzi 2002). With each item is associated an input parameter specifying if it has a fixed orientation or it can be rotated by 90 • . This problem contains as special cases the oriented and non-oriented 2BP. The new lower bound is based on the one described in Part I for the oriented 2BP. The computational results on the test problems derived from the literature show the effectiveness of the new proposed lower and upper bounds.
This paper considers the two-dimensional strip-packing problem (2SP) in which a set of rectangular items have to be orthogonally packed, without overlapping, into a strip of a given width and infinite height by minimizing the overall height of the packing. The 2SP is NP-hard in the strong sense and finds many practical applications. We propose reduction procedures, lower and upper bounds, and an exact algorithm for the 2SP. The new lower bounds are both combinatorial bounds and bounds derived from different relaxations of mathematical formulations of the 2SP. The new upper bounds are obtained by constructive heuristics based on different strategies to place the items into the strip. The new exact method is based on a branch-and-bound approach. Computational results on different sets of test problems derived from the literature show the effectiveness of the new lower and upper bounds and of the new exact algorithm.
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