Célia Paquay

A mixed integer programming formulation for the three‐dimensional bin packing problem deriving from an air cargo application

The present paper discusses the problem of optimizing the loading of boxes into containers. The goal is to minimize the unused volume. This type of problem belongs to the family of multiple bin size bin packing problems (MBSBPP). The approach includes an extensive set of constraints encountered in real-world applications in the three-dimensional case: the stability, the fragility of the items, the weight distribution, and the possibility to rotate the boxes. It also includes the specific situation in which containers are truncated parallelepipeds. This is typical in the field of air transportation. While most papers on cutting and packing problems describe ad hoc procedures, this paper proposes a mixed integer linear program. The validity of this model is tested on small instances.

MIP-based constructive heuristics for the three-dimensional Bin Packing Problem with transportation constraints

Abstract This article is about seeking a good feasible solution in a reasonable amount of computation time to the three-dimensional Multiple Bin Size Bin Packing Problem (MBSBPP). The MBSBPP studied considers additional constraints encountered in real world air transportation situations, such as cargo stability and the particular shape of containers. This MBSBPP has already been formulated as a Mixed Integer linear Programming problem, but as yet only poor results have been achieved for even fairly small problem sizes. The goal of the work this paper describes is to develop heuristics that are able to quickly provide good initial feasible solutions for the MBSBPP. Three methodologies are considered, which are based on the decomposition of the original problem into easier subproblems: the matheuristics Relax-and-Fix, Insert-and-Fix and Fractional Relax-and-Fix. They have been parametrised on real data sets and then compared to each other. In particular, two of these techniques show promising results in reasonable computational times.

A tailored two-phase constructive heuristic for the three-dimensional Multiple Bin Size Bin Packing Problem with transportation constraints

This paper considers the three-dimensional Multiple Bin Size Bin Packing Problem which consists in packing a set of cuboid boxes into containers of various shapes, while minimising unused space. The problem is extended to air cargo where the bins are Unit Load Devices, specially designed for fitting in aircraft. We developed a fast constructive heuristic able to manage the constraints to be met in transportation. The heuristic is split into two distinct phases. The first phase deals with the packing of boxes into identical bins using an extension of the Extreme Points which describe the possible interesting positions to accommodate boxes. During this phase, the fragility, stability and orientation of the boxes are taken into account as well as the special shape of the bins and their weight capacity. The second phase considers the multiple types of available bins. If necessary, the best loading pattern identified is enhanced with respect to weight distribution in post processing. After the description of the parametrisation, computational experiments are performed on data sets specially designed for this application. The heuristic requires only few seconds to achieve promising results in terms of filling rate.

The three-dimensional rectangular Multiple Bin Size Bin Packing Problem with transportation constraints: A case study in the field of air transportation

According to the International Air Transport Association and Air Transport Action Group, 51.3 million metric tons of goods were transported by airlines in 2014. To transport luggage, freight and mail, special containers, called Unit Load Devices (ULD), are used. The method of loading packages into ULDs represents a key element for cargo safety and aircraft weight and balance, as well as for the economy of airline companies.