A Linear Programming Approach to the Cutting Stock Problem---Part II

In this paper, the methods for stock cutting outlined in an earlier paper in this Journal [Opns Res 9, 849--859 1961] are extended and adapted to the specific full-scale paper trim problem. The paper describes a new and faster knapsack method, experiments, and formulation changes. The experiments include ones used to evaluate speed-up devices and to explore a connection with integer programming. Other experiments give waste as a function of stock length, examine the effect of multiple stock lengths on waste, and the effect of a cutting knife limitation. The formulation changes discussed are i limitation on the number of cutting knives available, n balancing of multiple machine usage when orders are being filled from more than one machine, and m introduction of a rational objective function when customers' orders are not for fixed amounts, but rather for a range of amounts. The methods developed are also applicable to a variety of cutting problems outside of the paper industry.