@article{BalasStephan2009, author = {Balas, Egon and Stephan, R{\"u}diger}, title = {On the cycle polytope of a directed graph and its relaxations}, series = {Networks}, volume = {54}, journal = {Networks}, number = {1}, doi = {10.1002/net.20303}, pages = {47 -- 55}, year = {2009}, language = {en} } @article{Stephan2009, author = {Stephan, R{\"u}diger}, title = {Facets of the (s,t)-p-path polytope}, series = {Discrete Appl. Math.}, volume = {157}, journal = {Discrete Appl. Math.}, number = {14}, doi = {10.1016/j.dam.2009.06.003}, pages = {3119 -- 3132}, year = {2009}, language = {en} } @article{KaibelStephan2010, author = {Kaibel, Volker and Stephan, R{\"u}diger}, title = {On cardinality constrained cycle and path polytopes}, series = {Math. Program.}, volume = {123}, journal = {Math. Program.}, number = {2 (A)}, doi = {10.1007/s10107-008-0257-2}, pages = {371 -- 394}, year = {2010}, language = {en} } @article{Stephan2010, author = {Stephan, R{\"u}diger}, title = {Cardinality constrained combinatorial optimization}, series = {Discrete Optim.}, volume = {7}, journal = {Discrete Optim.}, number = {3}, pages = {99 -- 113}, year = {2010}, language = {en} } @article{StephanSpiegelberg2010, author = {Stephan, R{\"u}diger and Spiegelberg, Ingo}, title = {On cardinality constrained polymatroids}, series = {Electronic Notes in Discrete Mathematics}, volume = {36}, journal = {Electronic Notes in Discrete Mathematics}, doi = {DOI: 10.1016/j.endm.2010.05.129}, pages = {1017 -- 1024}, year = {2010}, language = {en} } @article{HeinzSchlechteStephanetal., author = {Heinz, Stefan and Schlechte, Thomas and Stephan, R{\"u}diger and Winkler, Michael}, title = {Solving steel mill slab design problems}, series = {Constraints}, volume = {17}, journal = {Constraints}, number = {1}, doi = {10.1007/s10601-011-9113-8}, pages = {39 -- 50}, abstract = {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.}, language = {en} } @article{GroetschelStephan, author = {Gr{\"o}tschel, Martin and Stephan, R{\"u}diger}, title = {Characterization of Facets of the Hop Constrained Chain Polytope via Dynamic Programming}, series = {Discrete Applied Mathematics}, volume = {162}, journal = {Discrete Applied Mathematics}, doi = {10.1016/j.dam.2013.08.015}, pages = {229 -- 246}, language = {en} }