A branch-and-price algorithm for the two-dimensional level strip packing problem

A branch-and-price algorithm for the two-dimensional level strip packing problem

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Article ID: iaor200917405
Country: Germany
Volume: 6
Issue: 4
Start Page Number: 361
End Page Number: 374
Publication Date: Dec 2008
Journal: 4OR
Authors: , ,
Keywords: branch-and-cut, packing
Abstract:

The two–dimensional level strip packing problem (2LSPP) consists in packing rectangular items of given size into a strip of given width divided into levels. Items packed into the same level cannot be put on top of one another and their overall width cannot exceed the width of the strip. The objective is to accommodate all the items while minimizing the overall height of the strip. The problem is NP–hard and arises from applications in logistics and transportation. We present a set covering formulation of the 2LSPP suitable for a column generation approach, where each column corresponds to a feasible combination of items inserted into the same level. For the exact optimization of the 2LSPP we present a branch–and–price algorithm, in which the pricing problem is a penalized knapsack problem. Computational results are reported for benchmark instances with some hundreds items.

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