On the determination of the shortes path in a network having gains

The shortest path problem has been solved by FORD and FULKERSON [1] using a network method. COOK and HOLSEY [2] have given an algorithm for a generalization of te problem by applying dynamic programming to a network having time dependent edges. E. KLAFSZKY [3] has described a procedure using the flow method of FORD and FULKERSON which gives the shortest path in addition to the length of the path. CHARNES and RAIKE [4] applied linear programming to another generalization of te shortest path problem. This generalized problem is dealt with in this paper. The problem can be solved by the FORD and FULKERSON's procedure following the train of thought described by E. KLAFSZKY.