Hierarchical multi-objective decision systems and power-decentralized systems for general resource allocation problem
清孝 志水, 英太郎 相吉 · Institutional Repositories DataBase (IRDB) · 1980
We study optimization methods for hierarchical power-decentralized systems composed of a coordinating central system and plural semi-autonomous local systems in the lowerlevel, 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 hence a multiobjective system.The basic principle of planning is that the central system allocates resources so as to optimize its own objective, while the local ones optimize their own objectives using the given resources.The lower-level composes a multi-objective programming problem, where local decisionmakers minimize a vector objective function in cooperation.Thus, the lower level generates a set of noninferior solutions being parametric w. r. t. the given resources.The central decision-maker, then, chooses an optimal resource allocation and the best noninferior solution corresponding to it from among a set of resource-parametric noninferior solutions.Several theorems and computational methods are obtained based on parametric nonlinear mathematical programming using directional derivatives in order to treat nondifferentiable parametric functions.Note that, essentially, this paper is concerned with a combined theory for multi-objective decision problem and general resource allocation problem.