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.

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 with minimising unused space. The problem is extended to air cargo where bins are Unit Load Devices, especially designed for tting in aircraft. We developed a fast constructive heuristic able to manage the dierent constraints met in transportation. The heuristic is split into two distinct phases. The rst phase deals with the packing of boxes into identical bins using an extension of the Extreme Points. During this phase, the fragility, stability and orientations of the boxes are taken into account as well as the special shape of the bins and their weight capacity.The second phase takes into account the multiple types of available bins. If necessary, the best found loading pattern is nally enhanced with respect to weight distribution in a post processing. After parametrisation, computational experiments have been performed on data sets especially designed for this application. The heuristic requires really short computational times to achieve promising results.

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 (MIP), 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.

The Static and Stochastic Vehicle Routing Problem with Random Requests (SS-VRP-R) describes realistic operational contexts in which a fleet of vehicles has to serve customer requests appearing dynamically. Based on a probabilistic knowledge about the appearance of requests, the SS-VRP-R seeks a priori sequences of vehicle relocations, optimizing the expected responsiveness to the requests. In this paper, an existing computational framework, based on recourse strategies, is adapted to meet the objectives of the SS-VRP-R. The resulting models are applied to a real case study of the management of police units in Brussels. In this context, the expected average response time is minimized. To cope with the reality of the urban context, a time-dependent variant is also studied (TD-SS-VRP-R) in which the travel time between two locations is a function that depends on the departure time at the first location. Experiments confirm the contribution and the adaptability of the recourse strategies to a real-life, complex operational context. Provided an adequate solution method, simulation-based results show the high quality of the a priori solutions designed, even when compared to those designed by field experts. Finally, the experiments provide evidence that there is no potential gain in considering time-dependency in such an operational context.