MULTICOMMODITY NETWORK FLOWS.
PURDUE UNIV LAFAYETTE IND KRANNERT GRADUATE SCHOOL OF INDUSTRIAL ADMINISTRATION
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The purpose of this article is to survey the current literature on multicommodity network flows. The study of multicommodity flows is concerned with generalizing the results which are known for single commodity flows in networks. These results fall into three broad categories optimization, computation and structure. The optimization category includes the question of maximizing flow or minimizing cost in a network. The computation question involves finding algorithms for efficiently computing flows. And the structural results relate the flows to structural properties of the network e.g., the Max-flow Min-cut Theorem. Because of the added complexity of having many commodities, the results for multicommodity flows sometimes require methods different from those used for analogous single commodity results. As in the one-commodity case, the question of finding a maximal multicommodity flow can be stated as a linear programming problem. In general for n-commodity flow there is the question of feasibility. That is, not only do we wish to know how much flow can be achieved, but more specifically how much of each kind of commodity. Author
- Operations Research