A two-dimensional bin-packing problem with conflict penalties

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

In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...

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

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...

A one-dimensional bin packing problem with shelf divisions

Given bins of size B, non-negative values d and ∆, and a list L of items, each item e ∈ L with size se and class ce, we define a shelf as a subset of items packed inside a bin with total items size at most ∆ such that all items in this shelf have the same class. Two subsequent shelves must be separated by a shelf division of size d. The size of a shelf is the total size of its items plus the si...