The generalized assortment and best cutting stock length problems

This paper introduces two new one-dimensional cutting stock models: the generalized assortment problem (GAP) and the best cutting stock length (BSL) problem. These new models provide the potential to reduce waste to values lower than the optimum of current models, under the right management circumstances. In the GAP, management has a standard length and can select one or more of any additional custom stock lengths, and management wishes to minimize cutting stock waste. This model is different from existing models that assume that the selection is from a small fixed set of stock lengths. In the BSL problem, management chooses any number of custom stock lengths, but wishes to find the fewest custom stock lengths in order to have zero waste. Results show waste reductions of 80% with just one custom stock length compared with solutions from standard cutting stock formulations, when item lengths are long relative to the stock length. The models are most effective when the item lengths are nearly as long as the stock length. Solutions from the model have been implemented for a manufacturer. The model is easily generalized to allow multiple existing stock lengths and different costs.