TY - JOUR A1 - Balas, Egon A1 - Stephan, Rüdiger T1 - On the cycle polytope of a directed graph and its relaxations JF - Networks Y1 - 2009 U6 - https://doi.org/10.1002/net.20303 VL - 54 IS - 1 SP - 47 EP - 55 ER - TY - JOUR A1 - Kaibel, Volker A1 - Stephan, Rüdiger T1 - On cardinality constrained cycle and path polytopes JF - Math. Program. Y1 - 2010 U6 - https://doi.org/10.1007/s10107-008-0257-2 VL - 123 IS - 2 (A) SP - 371 EP - 394 ER - TY - JOUR A1 - Stephan, Rüdiger T1 - Facets of the (s,t)-p-path polytope JF - Discrete Appl. Math. Y1 - 2009 U6 - https://doi.org/10.1016/j.dam.2009.06.003 VL - 157 IS - 14 SP - 3119 EP - 3132 ER - TY - JOUR A1 - Stephan, Rüdiger T1 - Cardinality constrained combinatorial optimization JF - Discrete Optim. Y1 - 2010 VL - 7 IS - 3 SP - 99 EP - 113 ER - TY - JOUR A1 - Stephan, Rüdiger A1 - Spiegelberg, Ingo T1 - On cardinality constrained polymatroids JF - Electronic Notes in Discrete Mathematics Y1 - 2010 UR - http://www.sciencedirect.com/science/article/B75GV-50JJF7F-4K/2/2761e6edfcb262af0ba4856767d82a42 U6 - https://doi.org/DOI: 10.1016/j.endm.2010.05.129 VL - 36 SP - 1017 EP - 1024 ER - TY - JOUR A1 - Heinz, Stefan A1 - Schlechte, Thomas A1 - Stephan, Rüdiger A1 - Winkler, Michael T1 - Solving steel mill slab design problems JF - Constraints N2 - The steel mill slab design problem from the CSPLIB is a combinatorial optimization problem motivated by an application of the steel industry. It has been widely studied in the constraint programming community. Several methods were proposed to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called the multiple knapsack problem with color constraints, originated from the same industrial problem, was discussed in the integer programming community. In particular, a simple integer program for this problem has been given by Forrest et al. (INFORMS J Comput 18:129–134, 2006). The aim of this paper is to bring these different studies together. Moreover, we adapt the model of Forrest et al. (INFORMS J Comput 18:129–134, 2006) for the steel mill slab design problem. Using this model and a state-of-the-art integer program solver all instances of the steel mill slab library can be solved efficiently to optimality. We improved, thereby, the solution values of 76 instances compared to previous results (Schaus et al., Constraints 16:125–147, 2010). Finally, we consider a recently introduced variant of the steel mill slab design problem, where within all solutions which minimize the leftover one is interested in a solution which requires a minimum number of slabs. For that variant we introduce two approaches and solve all instances of the steel mill slab library with this slightly changed objective function to optimality. Y1 - 2012 U6 - https://doi.org/10.1007/s10601-011-9113-8 VL - 17 IS - 1 SP - 39 EP - 50 ER - TY - JOUR A1 - Grötschel, Martin A1 - Stephan, Rüdiger T1 - Characterization of Facets of the Hop Constrained Chain Polytope via Dynamic Programming JF - Discrete Applied Mathematics Y1 - 2014 U6 - https://doi.org/10.1016/j.dam.2013.08.015 VL - 162 SP - 229 EP - 246 ER -