This paper studies an optimal algorithm for the Maximum Origin-Destination Flor Path (MODFP) in an acyclic transportation network. We define a Pseudo-Flow each are so that it can give an upper bound to the total flow of a given path. And using the K-th Shortest Path algorithm we obtain upper bound of MODF which is decreasing as the number of searched path grows. Computational Complexity of optimal algorithm is O(K + m) $n_{2}$), K being the total number of searched path. We proved that the problem complexity of finding MODFP in an acyclic network is NP-hard, showing that the-satisfiability problem can be polynomialy reduced to this problem. And we estimated the average of the number K as being (m/n)$^{1,08}$ Exp (0.00689gm) from the computational experiments.