Directed hypergraphs have been introduced quite recently in connection with different application areas, such as propositional satisfiability, deductive data bases and Leontief substitution systems. In [Jeroslow, Martin, Rardin&Wang, 1989], the uncapacitated min-cost flow problem on hypergraphs is considered, and its properties are studied. Here we address the capacitated case, and show how the...

The minimum concave cost network flow problem (MCCNFP) has many applications in areas such as telecommunication network design, facility location, production and inventory planning, and traffic scheduling and control. However, it is a well known NP-hard problem, and all existing search based exact algorithms are not practical for networks with even moderate numbers of vertices. Therefore, the r...

3 Minimum cost network flow problem 5 3.1 Transportation problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 The maximum flow problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 The shortest path problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 The single source shortest paths . . . . . . . . . . . . . . . . ...

3 Minimum cost network flow problem 5 3.1 Transportation problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 The maximum flow problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 The shortest path problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 The single source shortest paths . . . . . . . . . . . . . . . . ...

3 Minimum cost network flow problem 5 3.1 Transportation problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 The maximum flow problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 The shortest path problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 The single source shortest paths . . . . . . . . . . . . . . . . ...