New reduction procedures and lower bounds for the two-dimensional bin packing problem with fixed orientation

The two-dimensional bin-packing problem (2BP) consists of minimizing the number of identical rectangles used to pack a set of smaller rectangles. In this paper, we propose new lower bounds for 2BP in the discrete case. They are based on the total area of the items after application of dual feasible functions (DFF). We also propose the new concept of data-dependent dual feasible functions (DDFF), which can also be applied to a 2BP instance. We propose two families of Discrete DFF and DDFF and show that they lead to bounds which strictly dominate those obtained previously. We also introduce two new reduction procedures and report computational experiments on our lower bounds. Our bounds improve on the previous best results and close 22 additional instances of a well-known established benchmark derived from literature.