Extending Two-Dimensional Bin Packing Problem: Consideration of Priority for Items

Two-Dimensional On-Line Bin Packing Problem with Rotatable Items

In this paper, we consider a two-dimensional version of the on-line bin packing problem, in which each rectangular item that should be packed into unit square bins is “rotatable” by 90 ◦ . Two on-line algorithms for solving the problem are proposed. The second algorithm is an extension of the 2rst algorithm, and the worst-case ratio of the second one is at least 2.25 and at most 2.565. c © 2002...

Two-Dimensional Bin Packing Problem with Guillotine Restrictions

Online Multi-dimensional Dynamic Bin Packing of Unit-Fraction Items

We study the 2-D and 3-D dynamic bin packing problem, in which items arrive and depart at arbitrary times. The 1-D problem was first studied by Coffman, Garey, and Johnson motivated by the dynamic storage problem. Bar-Noy et al. have studied packing of unit fraction items (i.e., items with length 1/k for some integer k ≥ 1), motivated by the window scheduling problem. In this paper, we extend t...

The Three-Dimensional Bin Packing Problem

The problem addressed in this paper is that of orthogonally packing a given set of rectangular-shaped items into the minimum number of three-dimensional rectangular bins. The problem is strongly NP-hard and extremely diicult to solve in practice. Lower bounds are discussed, and it is proved that the asymptotic worst-case performance ratio of the continuous lower bound is 1 8. An exact algorithm...

Three-dimensional bin packing problem with variable bin height

This paper studies a variant of the three-dimensional bin packing problem (3D-BPP), where the bin height can be adjusted to the cartons it packs. The bins and cartons to be packed are assumed rectangular in shape. The cartons are allowed to be rotated into any one of the six positions that keep the carton edges parallel to the bin edges. This greatly increases the difficulty of finding a good s...

Bin Packing Problem: Two Approximation Algorithms

The Bin Packing Problem is one of the most important optimization problems. In recent years, due to its NP-hard nature, several approximation algorithms have been presented. It is proved that the best algorithm for the Bin Packing Problem has the approximation ratio 3/2 and the time orderO(n), unlessP=NP. In this paper, first, a -approximation algorithm is presented, then a modification to FFD ...