## Abstract

In this work, we show how cardinality-related information for the set partitioning problem s represented within the simplex tableau and how a fractional solution can be interpreted in terms of unresolved solution cardinality. We include a cardinality row within the linear programming relaxation of the set partitioning problem to demonstrate the associated cardinality-related information present in the tableau. Working with a basic feasible solution, the cardinality row is shown to provide valuable information for branching along the cardinality dimension of the solution space of the problem. It is shown that cardinality information may be derived from the simplex tableau for any subset of structural variables in the problem. An illustrative example and computational results for problems from the literature are presented.

Original language | English (US) |
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Pages (from-to) | 49-60 |

Number of pages | 12 |

Journal | Operations Research/ Computer Science Interfaces Series |

Volume | 37 |

DOIs | |

State | Published - Jan 1 2007 |

## Keywords

- Cardinality
- Set partitioning
- Simplex tableau

## ASJC Scopus subject areas

- Computer Science(all)
- Management Science and Operations Research