In this paper, we introduce the shortest flow-generating path problem in the generalized network. As the simplest generalized network model, this problem captures many of the most salient core ingredients of the generalized network flows and so it provides both a benchmark and a point of departure for studying more complex generalized network models. We show that the generalized label-correcting algorithm for the shortest flow-generating path problem has O(mn) time complexity if it starts with a good point and also propose an O($n^3m^2$) algorithm for finding a good starting point. Hence, the shortest flow-generating path problem is solved in O($n^3m^2$) time.