DISTRIBUTION EXAMPLE Pure Network Model Linear Programming Model Solving the Model Variable External Flows A Generalized Network Model Side Constraints Vocabulary SPECIAL CASES Transportation Problem Assignment Problem Shortest Path Problem Maximum Flow Problem OTHER EXAMPLES A Transportation Problem with Costs of Manufacture and Revenue at Sale Multiperiod Operation Transformation of Flow Restrictions and Costs on Nodes Convex Costs and Concave Revenues Undirected Edges Elimination of Arc Lower Bounds Return to Modeling Home Page

The term network flow program describes a type of model that is a special case of the more general linear program. The class of network flow programs includes such problems as the transportation problem, the assignment problem, the shortest path problem, the maximum flow problem, the pure minimum cost flow problem, and the generalized minimum cost flow problem. It is an important class because many aspects of actual situations are readily recognized as networks and the representation of the model is much more compact than the general linear program. When a situation can be entirely modeled as a network, very efficient algorithms exist for the solution of the optimization problem, many times more efficient than linear programming in the utilization of computer time and space resources.