Combinatorial Approaches for the Trunk Packing Problem

In this thesis we consider a three-dimensional packing problem arising in industry. The task is to pack a maximum number of rigid boxes with side length ratios of 4 : 2 : 1 into an irregularly shaped container. Motivated by the structure of manually constructed packings so far, we pursue a discrete approach. We discretize the shape of the container as well as the set of possible box placements. This discrete packing problem can be reduced to a maximum stable set problem. First we formulate the problem as an integer linear program, which admittedly can only be solved to optimality within reasonable runtime for very small instances. Therefore, we present several heuristics based, for example, on the linear programming relaxation or on local search. Other heuristics generate tight packings for the core of the container, thereby reducing the problem to a set of smaller subproblems. We compare all presented algorithms on real data sets. We achieve very good results for the majority of instances and for some instances we even surpass the manually constructed solutions.