Optimizing strongly restricted loading problems with containers and pallets

Abstract

The entire logistics world is changing: the value chain, from raw material extraction to recycling, is experiencing a digital transformation that aims to increase data availability and simultaneously improve the connectivity of operational processes. This offers new opportunities for better and more realistic logistics planning that have yet to be investigated. This thesis concerns algorithms for strongly restricted loading problems in the context of the container loading problem combined with vehicle routing problems. Thus, new loading constraints are introduced as existing ones are improved – prompting the question of its costs and associated benefits. The costs are reflected by adapted objective functions. The benefits can be divided into three categories: higher security (for drivers, road users, parcels, and vehicles), efficient processes, as well as adherence to legal requirements. The thesis comprises a total of six scientific works dealing with this topic. Paper I1 describes various implementations of the Deepest-Bottom-Left-Fill algorithm, a widely used algorithm to solve the container loading problem. It is combined with an adaptive large neighborhood search heuristic to solve the vehicle routing problem. The computational experiments evaluate the best implementation and the impact of various constraints on the objective function and runtime. Paper II2 introduces formulas for considering axle weights for different truck types, e.g., varying axle configuration and trailer presence. It uses the same algorithms as the first paper. The computational experiments show that including the axle weights constraints has only a minor impact on the objective function but positive effects on the runtime. Therefore, the axle weights should always be considered in models for security reasons. Paper III3 focuses on analyzing complex loading constraints, presenting weaknesses of current formulations for vertical stability and stacking constraints, and introducing new constraints. The largest constraint set, consisting of geometry, orthogonality, rotation, vertical stability, stacking, reachability, axle weights, and balanced load constraints, is analyzed in the computational experiments. These constraints are evaluated independently concerning their impact on the objective function and runtime. A central conclusion is that the combined constraints’ impact is less than the sum of each constraint. Paper IV4 introduces a new formulation based on the science of statics for the vertical stability constraint, achieving the best results regarding impacts on the objective function and runtime compared to other common formulations. Paper V5 deals with calculating the manual effort for loading and unloading. This effort can be time-wise evaluated using the Methods-Time-Measurement (MTM) approach. This can also enable rearrangements of items so that the constraints dealing with fixed unloading sequences (e.g., LIFO) are replaced. The computational experiments show that this approach positively affects the objective values and the runtime. Paper VI6 introduces two tools for the combined optimization problem. The first one, “Solution Validator”, can check solutions concerning modifiable constraint sets, whereby all constraints evaluated in the previous papers are implemented. The second tool includes this Solution Validator and can visualize solutions for the routes, including distances and travel times. In addition, the container loading spaces, including the position of all boxes, are presented. Overall, each paper represents a single piece from a broader puzzle, highlighting constraints from different perspectives.