Cargo securing under multi-drop and axle weight constraints

This study emerges from a real-world cargo securing application to ensure safer road transportation and falls into the category of container loading problems with practical constraints. The literature has lacked efficient methods for the secure loading of items with non-identical dimensions, weights and rotations into containers while ensuring that the securing efforts necessary are minimal when also taking into account multi-drop and axle weight constraints. This paper puts forward a new way of ensuring cargo stability that gives rise to a novel combinatorial optimization problem, which is a generalization of the two-dimensional rectangular strip packing problem with orthogonal rotations. We formally demonstrate the intractability of the problem and provide a mixed integer programming formulation. The formulation is based on a discretization of the packing polyhedron, enabling us to model a range of complicated and practical constraints. A group of practical constraints tends to be large in number and makes it difficult to solve the formulation in a reasonable amount of time. In order to overcome this difficulty, we develop an exact algorithmic framework. This framework initially solves certain relaxations of the problem to obtain strong lower bounds before subsequently embedding those lower bounds into a branch-and-cut algorithm. The experimental study serves three purposes: (i) evaluating the performance of the algorithmic framework and the mathematical formulation to assess the merits of the two methods, (ii) identifying the characteristics of hard problem instances and (iii) extracting insights regarding challenges in cargo securing to help managers and practitioners in decision making.