Abstract
In a distribution network, materials or products that go through adecomposition process can be considered as flows entering a specialized node,called D-node, which distributes each decomposed flow along an outgoing arc.Flows on each arc emanating from a D-node have to obey a pre-specifiedproportional relationship, in addition to the capacity constraints. Thesolution procedures for calculating optimal flows over distribution networksin literature often assumes D-nodes to be disjoint, whereas in reality D-nodesmay often connect to each other and complicate the problem. In this paper, wepropose a polynomial-time network compaction scheme that compresses adistribution network into an equivalent one of smaller size, which can then bedirectly solved by conventional solution methods in related literature. Inorder to provide test cases of distribution networks containing D-nodes forcomputational tests in related research, we implement a random networkgenerator that produces a connected and acyclic distribution network in acompact form. Mathematical properties together with their proofs are alsodiscussed to provide more insights in the design of our generator.
Published Version
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