### Abstract

We consider optimization methods for hierarchical power-decentralized systems composed of a coordinating central system and plural semi-autonomous local systems in the lower level, each of which possesses a decision making unit. Such a decentralized system where both central and local systems possess their own objective function and decision variables is a multi-objective system. The central system allocates resources so as to optimize its own objective, while the local systems optimize their own objectives using the given resources. The lower level composes a multi-objective programming problem, where local decision makers minimize a vector objective function in cooperation. Thus, the lower level generates a set of noninferior solutions, parametric with respect to the given resources. The central decision maker, then, parametric with respect to the given resources. The central decision maker, then, chooses an optimal resource allocation and the best corresponding noninferior solution from among a set of resource-parametric noninferior solutions. A computational method is obtained based on parametric nonlinear mathematical programming using directional derivatives. This paper is concerned with a combined theory for the multi-objective decision problem and the general resource allocation problem.

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

Pages (from-to) | 517-533 |

Number of pages | 17 |

Journal | Journal of Optimization Theory and Applications |

Volume | 35 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1981 Dec |

### Fingerprint

### Keywords

- decentralized systems
- multi-objective systems
- nonlinear programming
- resource allocation
- Two-level planning

### ASJC Scopus subject areas

- Control and Optimization
- Applied Mathematics
- Management Science and Operations Research

### Cite this

*Journal of Optimization Theory and Applications*,

*35*(4), 517-533. https://doi.org/10.1007/BF00934930

**Hierarchical multi-objective decision systems for general resource allocation problems.** / Shimizu, K.; Aiyoshi, E.

Research output: Contribution to journal › Article

*Journal of Optimization Theory and Applications*, vol. 35, no. 4, pp. 517-533. https://doi.org/10.1007/BF00934930

}

TY - JOUR

T1 - Hierarchical multi-objective decision systems for general resource allocation problems

AU - Shimizu, K.

AU - Aiyoshi, E.

PY - 1981/12

Y1 - 1981/12

N2 - We consider optimization methods for hierarchical power-decentralized systems composed of a coordinating central system and plural semi-autonomous local systems in the lower level, each of which possesses a decision making unit. Such a decentralized system where both central and local systems possess their own objective function and decision variables is a multi-objective system. The central system allocates resources so as to optimize its own objective, while the local systems optimize their own objectives using the given resources. The lower level composes a multi-objective programming problem, where local decision makers minimize a vector objective function in cooperation. Thus, the lower level generates a set of noninferior solutions, parametric with respect to the given resources. The central decision maker, then, parametric with respect to the given resources. The central decision maker, then, chooses an optimal resource allocation and the best corresponding noninferior solution from among a set of resource-parametric noninferior solutions. A computational method is obtained based on parametric nonlinear mathematical programming using directional derivatives. This paper is concerned with a combined theory for the multi-objective decision problem and the general resource allocation problem.

AB - We consider optimization methods for hierarchical power-decentralized systems composed of a coordinating central system and plural semi-autonomous local systems in the lower level, each of which possesses a decision making unit. Such a decentralized system where both central and local systems possess their own objective function and decision variables is a multi-objective system. The central system allocates resources so as to optimize its own objective, while the local systems optimize their own objectives using the given resources. The lower level composes a multi-objective programming problem, where local decision makers minimize a vector objective function in cooperation. Thus, the lower level generates a set of noninferior solutions, parametric with respect to the given resources. The central decision maker, then, parametric with respect to the given resources. The central decision maker, then, chooses an optimal resource allocation and the best corresponding noninferior solution from among a set of resource-parametric noninferior solutions. A computational method is obtained based on parametric nonlinear mathematical programming using directional derivatives. This paper is concerned with a combined theory for the multi-objective decision problem and the general resource allocation problem.

KW - decentralized systems

KW - multi-objective systems

KW - nonlinear programming

KW - resource allocation

KW - Two-level planning

UR - http://www.scopus.com/inward/record.url?scp=0019687875&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0019687875&partnerID=8YFLogxK

U2 - 10.1007/BF00934930

DO - 10.1007/BF00934930

M3 - Article

AN - SCOPUS:0019687875

VL - 35

SP - 517

EP - 533

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

SN - 0022-3239

IS - 4

ER -