DOI: 10.1007/s10288-002-0005-z 4OR 1: (2002) Regular paper The Two-Dimensional Finite Bin Packing Problem Part I: New lower bounds for the oriented case Marco A. Boschetti ⋆ and Aristide Mingozzi Department of Mathematics, University of Bologna, Bologna, Italy. e-mail: {boschett, mingozzi}@csr.unibo.it Received: February 2002 / Revised version: September 2002 Abstract. The Two-Dimensional Finite Bin Packing Problem (2BP) consists of determining the minimum number of large identical rectangles, bins, that are re- quired for allocating without overlapping a given set of rectangular items. The items are allocated into a bin with their edges always parallel or orthogonal to the bin edges. The problem is strongly NP-hard and finds many practical applications. In this paper we describe new lower bounds for the 2BP where the items have a fixed orientation and we show that the new lower bounds dominate two lower bounds proposed in the literature. These lower bounds are extended in Part II (see Boschetti and Mingozzi (2002)) for a more general version of the 2BP where some items can be rotated by 90 ◦ . Moreover, in Part II a new heuristic algorithm for solving both versions of the 2BP is presented and computational results on test problems from the literature are given in order to evaluate the effectiveness of the proposed lower bounds. Keywords: Cutting and Packing, Lower Bounds, Combinatorial Optimization 1 Introduction The Two-Dimensional Finite Bin Packing Problem (2BP) consists of determining the minimum number of large identical rectangles, bins, that are required for al- locating without overlapping a given set of rectangular items, each with a given ⋆ Corresponding author: Marco A. Boschetti, Department of Mathematics, University of Bologna, Via Sacchi 3, 47023 Cesena, Italy, Tel. +39-0547-642806, Fax +39-0547-610054. 4OR Quarterly Journal of the Belgian, French and Italian Operations Research Societies © Springer-Verlag 2002