Roll assortment optimization in a paper mill: An integer programming approach

Fine paper mills produce a variety of paper grades to satisfy demand for a large number of sheeted products. Huge reels of different paper grades are produced on a cyclical basis on paper machines. These reels are then cut into rolls of smaller size which are then either sold as such, or sheeted into finished products in converting plants. A huge number of roll sizes would be required to cut all finished products without trim loss and they cannot all be inventoried. An assortment of rolls is inventoried with the implication that the sheeting operations may yield trim loss. The selection of the assortment of roll sizes to stock and the assignment of these roll sizes to finished products have a significant impact on performances. This paper presents a model to decide the parent roll assortment and assignments to finished products based on these products demand processes, desired service levels, trim loss and inventory holding costs. Risk pooling economies made by assigning several finished products to a given roll size is a fundamental aspect of the problem. The overall model is a binary non-linear program. Two solution methods are developed: a branch and price algorithm based on column generation and a fast pricing heuristic, and a marginal cost heuristic. The two methods are tested on real data and also on randomly generated problem instances. The approach proposed was implemented by a large pulp and paper company.