An integer programming approach for the 2-schemes strip cutting problem with a sequencing constraint Silvina Lucero • Javier Marenco • Federico Martı ´nez Received: 9 August 2013 / Accepted: 3 September 2014 Ó Springer Science+Business Media New York 2014 Abstract We study integer programming formulations for the 2-schemes strip cutting problem with a sequencing constraint (2-SSCPsc) considered by Rinaldi and Franz. The 2-SSCPsc arises in the context of corrugated cardboard production, which involves cutting strips of large lengths into rectangles of at most (usually) two different lengths. Because of buffer restrictions, in the 2-SSCPsc these strips must be sequenced in such a way that, at any moment, at most two types of items are in production and not completed yet. This problem is NP-hard. We present four integer programming for- mulations for this problem, and our computational experiments with real-life instances show that one of them has a very tight integrality gap. We propose a heuristic pro- cedure based on this formulation and present computational experience showing that this procedure finds very good primal solutions in small running times. Keywords Corrugated cardboard  Integer programming  Sequencing 1 Introduction A corrugator is a machine that produces rectangular pieces of corrugated cardboard, called items. Items have different sizes, and for each item size a number of pieces has to be produced. A typical corrugator glues together two or more rolls of paper S. Lucero  J. Marenco (&)  F. Martı ´nez Computer Science Department, FCEyN, University of Buenos Aires, Int. Gu ¨iraldes y Av. Cantilo, Pabello ´n I, 1428 Ciudad de Buenos Aires, Argentina e-mail: jmarenco@dc.uba.ar S. Lucero e-mail: svlucero@dc.uba.ar F. Martı ´nez e-mail: femartinez@dc.uba.ar 123 Optim Eng DOI 10.1007/s11081-014-9264-8