The transportation problem has offered two mathematical facets: (1) as a specialized type of linear programming problem, (2) as a method of representation of some combinatorial problems. In this paper a third aspect of the mathematical properties of the transportation problem is developed. It is shown that the same mathematical framework can be extended beyond pair-wise connections, to the determination of optimum linked paths over a series of points. This extension although viewed here as a linear programming problem, takes advantage of the combinatorial aspect of the transportation problem, and applications may arise which, like the assignment problem, appear to be combinatorial problems, but which can be solved by linear programming.