Modeling of a Rich Bin Packing Problem from Industry

We present and share the experience of modeling a real-life optimization problem. This exercise in modeling is a text book example of how a naive, straightforward mixed-integer modeling approach leads to a highly intractable model, while a deeper problem analysis leads to a non-standard, much stronger model. Our development process went from a weak model with burdensome run times, via meta-heuristics and column generation, to end up with a strong model which solves the problem within seconds. The problem in question deals with the challenges of planning the order-driven continuous casting production at the Swedish steel producer SSAB. We study the cast planning problem, where the objective is to minimize production waste which unavoidably occurs as orders of different steel grades are cast in sequence. This application can be categorised as a rich bin packing problem.