J. Martinovic, G. Scheithauer, V. de Carvalho
A Comparative Study of the Arcflow Model and the One-Cut Model for one-dimensional Cutting Stock Problems

We consider the one-dimensional cutting stock problem which consists of determining the minimum number of given large stock rolls that has to be cut to satisfy the demands of certain smaller item lengths. Besides the standard pattern-based approach of Gilmore and Gomory, containing an exponentially large number of variables, several pseudo-polynomial formulations were proposed in the last decades. In particular, much research has been dealt with arcflow models, their relationship to the standard model, and possible reduction methods, whereas the one-cut approach did not attract that much scientific interest yet. In this paper, we aim to compare both alternative formulations from a theoretical and numerical point of view. Therefore, we first present how reduction methods, partly originating from arcflow considerations, can successfully be transferred to the one-cut context. Furthermore, we derive relations between the numbers of variables and constraints in both models, and investigate their influences in numerical simulations. As a theoretical main contribution, we prove the equivalence of the
PDF, (Preprint MATH-NM-03-2017, TU Dresden, January 2017, 32 p.)