### Abstract

One approach in stochastic programming involves minimizing the expectation of cost, which includes a recourse function to represent the penalties for constraint violation. A known solution for such problems uses the L-shaped method based on the Benders decomposition. Stochastic programming problems that take the variance of the recourse function into account are non-convex problems, and an exact solution based on the branch-and-bound method has previously been demonstrated. However, since there are cases where the lower bound for the variance of the recourse function used in the branch-and-bound method is not effective, we present a new lower bound and demonstrate the effectiveness of the resulting solution by a numerical experiment.

Original language | English |
---|---|

Pages (from-to) | 1851-1856 |

Number of pages | 6 |

Journal | ICIC Express Letters |

Volume | 8 |

Issue number | 7 |

Publication status | Published - 2014 |

Externally published | Yes |

### Fingerprint

### Keywords

- Branch-and-bound
- Lower bound
- Stochastic programming

### ASJC Scopus subject areas

- Computer Science(all)
- Control and Systems Engineering

### Cite this

*ICIC Express Letters*,

*8*(7), 1851-1856.

**Deriving a new lower bound in stochastic programming problem considering variance.** / Shiina, Takayuki; Tagaya, Yu; Morito, Susumu; Imaizumi, Jun.

Research output: Contribution to journal › Article

*ICIC Express Letters*, vol. 8, no. 7, pp. 1851-1856.

}

TY - JOUR

T1 - Deriving a new lower bound in stochastic programming problem considering variance

AU - Shiina, Takayuki

AU - Tagaya, Yu

AU - Morito, Susumu

AU - Imaizumi, Jun

PY - 2014

Y1 - 2014

N2 - One approach in stochastic programming involves minimizing the expectation of cost, which includes a recourse function to represent the penalties for constraint violation. A known solution for such problems uses the L-shaped method based on the Benders decomposition. Stochastic programming problems that take the variance of the recourse function into account are non-convex problems, and an exact solution based on the branch-and-bound method has previously been demonstrated. However, since there are cases where the lower bound for the variance of the recourse function used in the branch-and-bound method is not effective, we present a new lower bound and demonstrate the effectiveness of the resulting solution by a numerical experiment.

AB - One approach in stochastic programming involves minimizing the expectation of cost, which includes a recourse function to represent the penalties for constraint violation. A known solution for such problems uses the L-shaped method based on the Benders decomposition. Stochastic programming problems that take the variance of the recourse function into account are non-convex problems, and an exact solution based on the branch-and-bound method has previously been demonstrated. However, since there are cases where the lower bound for the variance of the recourse function used in the branch-and-bound method is not effective, we present a new lower bound and demonstrate the effectiveness of the resulting solution by a numerical experiment.

KW - Branch-and-bound

KW - Lower bound

KW - Stochastic programming

UR - http://www.scopus.com/inward/record.url?scp=84903439899&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903439899&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 1851

EP - 1856

JO - ICIC Express Letters

JF - ICIC Express Letters

SN - 1881-803X

IS - 7

ER -