In this presentation we describe a real life application of a container loading problem for a children’s shoes manufacturer. First, we choose the appropriate shoe box for each pair of shoes depending on the model and size before production starts. Then, the shoe boxes are packed in several cardboard boxes with variable dimensions. We present an integer programming model that chooses the shoe boxes for each model size, and a MINLP model which decides how to pack the shoe boxes and the size of cardboard boxes. This container loading problem is classified as open dimension problem, with three open dimensions. We approximate the MINLP model with a MILP and we compare it by using BARON on the former model and we run CPLEX on the latter model.

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