# Hyperflow Models

We consider the Minimum cost hyperflow problem, a generalization of the
minimum cost flow problems on standard and on generalized graphs. In order
to solve this problem, a specialization of the primal Simplex Algorithm,
named the Hypergraph Simplex Algorithm, has been recently proposed. Here,
the results of a wide experimentation on random hypergraphs and on some
kinds of
structured hypergraphs are reported. In the experimentation, a C implementation
of the Hypergraph Simplex Algorithm has been compare wth the primal version
of CPLEX code, by obtaining rather interesting results. In fact, when the
hypergraph size increases, our code runs faste than CPLEX; in particular,
its solution time is a rather slow increasing fnction of the hypergraph size.
The problem under consideration has very interesting applications, which
can be modelled and solved in terms of hypergraph flows. These include
Multicommodity flows and applications in the area of flexible manufacturing
systems, like the One-Dimensional Cutting Stock Problem and Assembly Problems.
In particular, it is shown how to model Assembly Problems with a given degree,
say k, of parallelism (i.e. when k parallel identical machinesare available
for the execution of the operations) in terms of hyperflows. Finally, some
Economic Applications are formulated and interpreted in terms of minimum cost
hyperflow problems.