We address a 1-dimensional cutting stock problem where, in addition to trim-loss minimization, we require that the set of cutting patterns forming the solution can be sequenced so that the number of stacks of parts maintained open throughout the process never exceeds a given $s$. For this problem, we propose a new integer linear programming formulation whose constraints grow quadratically with the number of distinct part types.
Tech. Rep. TRCS 007/2010, Dip. di Informatica, Università degli Studi dell'Aquila