A practical instance of a one-dimensional cutting stock problem arising frequently in the paper industry is considered. Given a set of raw paper rolls of known length and width, a set of product paper rolls of known length (equal to the length of raw paper rolls) and width, practical cutting constraints on a single cutting machine, and demand orders for all products, the problem requires the determination of an optimal cutting schedule to maximize the overall cutting process profitability while satisfying all demands and cutting constraints. A purely mixed-integer linear programing (MILP) model is developed that does not require the a priori determination of all feasible cutting combinations. A complex objective function including trim loss, overproduction, knife (pattern) changeover costs, and format (raw material type) changeover costs is optimized. A salient feature of the model is that intermediate demand orders are taken into consideration as an integral part of the formulation. A number of example problems, including an industrial case study, are employed to illustrate the applicability and computational performance of the proposed method.