Analysis of a multi-commodity sharing problem for a distribution system

Abstract

This thesis considers a sharing problem for distributing a given quantity of resources to all destinations equitably under arc capacity constraints in a distribution network. The objective is to minimize the squared sum of differences between the perfectly equitable distribution quantity and the actual flow amount to each destination. With this objective, both the single and two resources commodities sharing problems are considered. For the case of the single resource, a solution property is characterized and then used to derive an optimal solution algorithm. For the case of the two resources, a heuristic procedure is proposed and tested for its efficiency with numerical examples.