One-dimensional cutting stock with a limited number of open stacks: Bounds and solutions from a new integer linear programming model

We address a one-dimensional cutting stock problem where, in addition to trim-loss minimization, cutting patterns must be sequenced so that no more than s different part types are in production at any time. We propose a new integer linear programming formulation whose constraints grow quadratically with the number of distinct part types and whose linear relaxation can be solved by a standard column generation procedure. The formulation allowed us to solve problems with 20 part types for which an optimal solution was unknown.