A branch‐and‐cut algorithm for the irregular strip packing problem with uncertain demands

This work presents a tailored branch‐and‐cut algorithm for the two‐dimensional irregular strip packing problem with uncertain demand for the items to be cut. A two‐stage stochastic programming model is developed, considering a discrete and finite set of scenarios. The strip is discretized over a mesh of points in the model and includes constraints to ensure items are non‐overlapping based on the concepts of inner‐fit raster and no‐fit raster. The algorithm considers lower and upper bounds from a heuristic based on the variable neighborhood search. This heuristic is also used during optimization to obtain new solutions and help to prune unsatisfactory nodes. The numerical results indicate the effectiveness of the proposed algorithm when observing other exact algorithms on the same problem without uncertainty. The algorithm can also provide optimal solutions for instances with uncertainty having more than 60 scenarios within some hours of execution. Besides, the conclusions show it is preferable to handle uncertainty to achieve minimum cost decisions.