### Abstract

Although parametric optimization with uncertainties on the objective function (OF) or on the so-called "right-hand-side" (RHS) of the constraints has been addressed successfully in recent papers, very little work exists on the same with uncertainties on the left-hand-side (LHS) of the constraints or in the coefficients of the constraint matrix. The goal of this work has been to develop a systematic method to solve such parametric optimization problems. This is a very complex problem and we have begun with the simplest of optimization problems, namely the linear programming problem with a single parameter on the LHS. This study reviews the available work on parametric optimization, describes the challenges and issues specific to LHS parametric linear programming (LHS-pLP), and presents a solution algorithm using some classic results from matrix algebra.

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

Pages (from-to) | 31-40 |

Number of pages | 10 |

Journal | Computers and Chemical Engineering |

Volume | 60 |

DOIs | |

Publication status | Published - 10 Jan 2014 |

Externally published | Yes |

### Keywords

- Left-hand-side
- Linear program
- LP
- Parametric programming
- Uncertainty

### Cite this

}

*Computers and Chemical Engineering*, vol. 60, pp. 31-40. https://doi.org/10.1016/j.compchemeng.2013.08.005

**Parametric optimization with uncertainty on the left hand side of linear programs.** / Khalilpour, Rajab; Karimi, I. A.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Parametric optimization with uncertainty on the left hand side of linear programs

AU - Khalilpour, Rajab

AU - Karimi, I. A.

PY - 2014/1/10

Y1 - 2014/1/10

N2 - Although parametric optimization with uncertainties on the objective function (OF) or on the so-called "right-hand-side" (RHS) of the constraints has been addressed successfully in recent papers, very little work exists on the same with uncertainties on the left-hand-side (LHS) of the constraints or in the coefficients of the constraint matrix. The goal of this work has been to develop a systematic method to solve such parametric optimization problems. This is a very complex problem and we have begun with the simplest of optimization problems, namely the linear programming problem with a single parameter on the LHS. This study reviews the available work on parametric optimization, describes the challenges and issues specific to LHS parametric linear programming (LHS-pLP), and presents a solution algorithm using some classic results from matrix algebra.

AB - Although parametric optimization with uncertainties on the objective function (OF) or on the so-called "right-hand-side" (RHS) of the constraints has been addressed successfully in recent papers, very little work exists on the same with uncertainties on the left-hand-side (LHS) of the constraints or in the coefficients of the constraint matrix. The goal of this work has been to develop a systematic method to solve such parametric optimization problems. This is a very complex problem and we have begun with the simplest of optimization problems, namely the linear programming problem with a single parameter on the LHS. This study reviews the available work on parametric optimization, describes the challenges and issues specific to LHS parametric linear programming (LHS-pLP), and presents a solution algorithm using some classic results from matrix algebra.

KW - Left-hand-side

KW - Linear program

KW - LP

KW - Parametric programming

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=84884139176&partnerID=8YFLogxK

U2 - 10.1016/j.compchemeng.2013.08.005

DO - 10.1016/j.compchemeng.2013.08.005

M3 - Article

VL - 60

SP - 31

EP - 40

JO - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

SN - 0098-1354

ER -