Fuzzy resource allocation
type: Item
instance of: scholarly article
title: Fuzzy resource allocation
zbMATH Open document ID: 0603.90083
DOI: 10.1016/0165-0114(86)90053-9
author: K. M. Mjelde
published in: Fuzzy Sets and Systems
publication date: 1986-01-01T00:00:00Z
review text: The allocation problem of J resources to I tasks is studied by means of a fuzzy set (FS) theory approach. The total consumption \(y_ j\) of resource j is described by an FS \(A_ j\) and another FS \(B_ j\) permits to model the effectiveness of activity k. Take \(\mu_ j\) and \(r_ k\) as the corresponding membership functions. It is assumed that \(\mu_ j\) is a continuous decreasing function and \(r_ k\) a continuous increasing one. A fuzzy decision in this case, is related to an allocation matrix x with membership function \(z(x)\) and the objective is to obtain a decision \(\bar x\) such that \(z(\bar x)\) is maximum. This is an optimization problem D. A solution algorithm is proposed for obtaining \(z(\bar x)\) in an other optimization problem DA. A lemma proves that the optimal solution x' of DA yields the optimum of D and if \(\bar x\) has the objective value \(\bar z\) the matrices and the membership functions of D and DA coincide. A theorem states that an optimal solution of D can be determined by an algorithm which is developed in this paper. A numerical example illustrates the behaviour of it. If \(\mu_ j\) and \(r_ k\) are concave, for any j and k, the solution of D is obtained by using linear programming techniques. Under certain situations the hypothesis of ''strictly decreasing'' function may be removed for the \(\mu_ j\)'s. Some applications to specific types of resource allocation problems are given.
Mathematics Subject Classification ID: 90B50
Mathematics Subject Classification ID: 90C99
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 3974718
zbMATH Keywords: fuzzy decision
zbMATH Keywords: fuzzy resources
zbMATH Keywords: fuzzy activities
zbMATH Keywords: resource allocation
reviewed by: Carlos Narciso Bouza Herrera
MaRDI profile type: Publication
full work available at URL: 0165-0114(86)90053-9
OpenAlex ID: W2049405903
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description: scientific article; zbMATH DE number 3974718