Three-dimensional truck and container loading problems arise in logistics applications, namely in the transportation sector. Parallelepiped boxes, with a length, a width and a height, have to packed inside an also parallelepiped empty space (the interior of a container or a truck). The goal is either to maximize the container/truck volume utilization or to minimize the number of containers/trucks necessary to transport all cargo. The third dimension naturally increases the difficulty in solving the problem, regarding both the combinatorial and geometric components of the problem. But what makes this problem distinctive from the previous Cutting and Packing problems is the big number of practical constraints that have to addressed: this-side-up, multi-drop distribution imposing last-in-first-out arrangements of the cargo, cargo stability, weight limit, weight per axle, load bearing capacity of each box, etc. This problem is very much integrated with other logistics related problems as vehicle routing, capacity assignment or warehouse management, including transhipment, cargo consolidation, etc.

According to studies and surveys involving logistics companies, the main source of uncertainty in this sector are the boxes dimensions. Although cargo has to be declared in advance, it is frequent that the actual box dimensions are different from the declared dimensions. The second source of uncertainty is related to delays in having the cargo available for loading at the warehouses, and even no-shows. This means that trucks leave with an incomplete load.

These unexpected changes not only question the optimality of the generated solutions but also require replanning and modifying packing plans. The goal of this task is to incorporate uncertainty in box dimensions in the three-dimensional packing problem, and, if results of task 1 support this goal, to deal with the multi-period version of the problem, dealing with uncertainty on the date on which cargo will be available for transportation. The aim is the generation of packing plans more robust regarding the variability induced by uncertainty and, when replanning is needed, the changes in the already defined packing plans are minimized: robust planning and optimized replanning.