A compaction scheme and generator for distribution networks

In a distribution network, materials or products that go through a decomposition process can be considered as ows entering a specialized node, called D-node, which distributes each decomposed ow along an outgoing arc. Flows on each arc emanating from a D-node have to obey a pre-specified proportional relationship, in addition to the capacity constraints. The solution procedures for calculating optimal ows over distribution networks in litera- ture often assumes D-nodes to be disjoint, whereas in reality D-nodes may often connect to each other and complicate the problem. In this paper, we proposea polynomial-time network compaction scheme that compresses a distribution network into an equivalent one of smaller size, which can then be directly solved by conventional solution methods in related literature. In order to provide test cases of distribution networks containing D-nodes for computational tests in related research, we implement a random network generator that produces a connected and acyclic distribution network in a compact form. Mathematical properties together with their proofs are also discussed to provide more insights in the design of our generator.