### 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) |
---|---|

Pages (from-to) | 49-60 |

Number of pages | 12 |

Journal | Operations Research/ Computer Science Interfaces Series |

Volume | 37 |

State | Published - Dec 1 2007 |

### Fingerprint

### Keywords

- Cardinality
- Set partitioning
- Simplex tableau

### ASJC Scopus subject areas

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

### Cite this

*Operations Research/ Computer Science Interfaces Series*,

*37*, 49-60.

**Cardinality and the simplex tableau for the set partitioning problem.** / Joseph, Anito; Baker, Edward K.

Research output: Contribution to journal › Article

*Operations Research/ Computer Science Interfaces Series*, vol. 37, pp. 49-60.

}

TY - JOUR

T1 - Cardinality and the simplex tableau for the set partitioning problem

AU - Joseph, Anito

AU - Baker, Edward K.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

KW - Cardinality

KW - Set partitioning

KW - Simplex tableau

UR - http://www.scopus.com/inward/record.url?scp=84888594877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888594877&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84888594877

VL - 37

SP - 49

EP - 60

JO - Operations Research/ Computer Science Interfaces Series

JF - Operations Research/ Computer Science Interfaces Series

SN - 1387-666X

ER -