Models and algorithms for three-stage two-dimensional bin packing

Models and algorithms for three-stage two-dimensional bin packing

We consider the three-stage two-dimensional bin packing problem (2BP) which occurs in real-world applications such as glass, paper, or steel cutting. We present new integer linear programming formulations: Models for a restricted version and the original version of the problem are developed. Both involve polynomial numbers of variables and constraints only and effectively avoid symmetries. Thos...

Algorithms for Two-Dimensional Bin Packing and Assignment Problems

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...

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...

A Three-dimensional Bin Packing Algorithm

In this paper an approximation algorithm for the three-dimensional bin packing problem is proposed and its performance bound is investigated. To obtain such a bound a modified bin packing algorithm is considered for a two-dimensional problem with bounded bin and its area utilization is estimated. Finally, a hard example gives a lower bound of the performance bound. '