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.