## Solving steel mill slab design problems

Please always quote using this URN: urn:nbn:de:0297-zib-14089

- 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. The aim of this paper is to bring these different studies together. Moreover, we adapt the model of Forrest et al. 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. 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.

Author: | Stefan Heinz, Thomas Schlechte, Rüdiger Stephan, Michael Winkler |
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Document Type: | ZIB-Report |

Tag: | binpacking with side constraints; integer programming; multiple knapsack problem with color constraints; set partitioning; steel mill slab design problem |

MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C90 Applications of mathematical programming | |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] | |

Date of first Publication: | 2011/09/29 |

Series (Serial Number): | ZIB-Report (11-38) |

ISSN: | 1438-0064 |

Published in: | Appeared in: Constraints 17 (2012) 39-50 |

DOI: | http://dx.doi.org/10.1007/s10601-011-9113-8 |