The weighted linear optimal distribution problem and applications
type: Item
instance of: scholarly article
title: The weighted linear optimal distribution problem and applications
zbMATH Open document ID: 0728.90033
author: A. Mehailia
published in: Bulletin of the Iranian Mathematical Society
publication date: 1990-01-01T00:00:00Z
review text: Let G be a connected network where each arc has a capacity interval \(C(j)=[c^-(j),c^+(j)]\) and each node i has a supply b(i), where \(b(N)=0\). It assumes that the cost of the flux \(x(j)\in [c^- (j),c^+(j)]\) is given by a linear expression \(d(j)x(j)+r(j)\), where d(j) and r(j) are constants associated with the arc j. The following optimality problem is studied: \[ \text{ minimize } \sum_{j\in A}d(j)x(j)+r(j)\quad =\quad dx\quad +\quad (text{constant}) \] over all flows x such that \(c^-(j)\leq x(j)\leq c^+(j)\) for all \(j\in A\) and \[ \sum_{j\in A}e(i,j)p(j)x(j)\quad =\quad b(i)\text{ for all } i\in N, \] where A is the set of arcs and p(j) is a constant associated with the arc j.
reviewed by: V.Peteanu
Mathematics Subject Classification ID: 90B10
zbMATH DE Number: 4204090
zbMATH Keywords: connected network
zbMATH Keywords: capacity interval
zbMATH Keywords: optimality problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4204090