On the two-dimensional Knapsack Problem

Authors:
Alberto Caprara;Michele Monaci
Affiliations:
Dipartimento di Elettronica, Informatica e Sistemistica, Universití di Bologna, Viale Risorgimento, 2, I-40136, Bologna, Italy;Dipartimento di Elettronica, Informatica e Sistemistica, Universití di Bologna, Viale Risorgimento, 2, I-40136, Bologna, Italy
Venue:
Operations Research Letters
Year:
2004

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Abstract

We address the two-dimensional Knapsack Problem (2KP), aimed at packing a maximum-profit subset of rectangles selected from a given set into another rectangle. We consider the natural relaxation of 2KP given by the one-dimensional KP with item weights equal to the rectangle areas, proving the worst-case performance of the associated upper bound, and present and compare computationally four exact algorithms based on the above relaxation, showing their effectiveness.