A SAT encoding for Multi-dimensional Packing Problems

International audienceThe Orthogonal Packing Problem (OPP) consists in determining if a set of items can be packed into a given container. This decision problem is NP-complete. S. P. Fekete et al. modelled the problem in which the overlaps between the objects in each dimension are represented by interval graphs. In this paper we propose a SAT encoding of Fekete et al. characterization. Some results are presented, and the efficiency of this approach is compared with other SAT encodings

Solving Pallet loading Problem with Real-World Constraints

Efficient cargo packing and transport unit stacking play a vital role in enhancing logistics efficiency and reducing costs in the field of logistics. This article focuses on the challenging problem of loading transport units onto pallets, which belongs to the class of NP-hard problems. We propose a novel method for solving the pallet loading problem using a branch and bound algorithm, where there is a loading order of transport units. The derived algorithm considers only a heuristically favourable subset of possible positions of the transport units, which has a positive effect on computability. Furthermore, it is ensured that the pallet configuration meets real-world constraints, such as the stability of the position of transport units under the influence of transport inertial forces and gravity.Comment: 8 pages, 1 figure, project report pape

The two-dimensional bin packing problem with variable bin sizes and costs

AbstractThe two-dimensional variable sized bin packing problem (2DVSBPP) is the problem of packing a set of rectangular items into a set of rectangular bins. The bins have different sizes and different costs, and the objective is to minimize the overall cost of bins used for packing the rectangles. We present an integer-linear formulation of the 2DVSBPP and introduce several lower bounds for the problem. By using Dantzig–Wolfe decomposition we are able to obtain lower bounds of very good quality. The LP-relaxation of the decomposed problem is solved through delayed column generation, and an exact algorithm based on branch-and-price is developed. The paper is concluded with a computational study, comparing the tightness of the various lower bounds, as well as the performance of the exact algorithm for instances with up to 100 items