  The rail freight flow assignment (RFFA) is a key point of network design and
operations management. Unlike a road network, the freight flow assignment
pattern in a rail system has unique characteristics, and the most significant
one is the tree-shaped path. More specifically, when two or more shipments
arrive at a rail yard, those intended for the same destination will be treated
as a single freight flow and be shipped through the same path during the
remainder of the trip, regardless of their origins. This paper reveals the
forming mechanism of the tree-shaped path from the perspective of rail yard
operations, and develops a nonlinear programming model for the RFFA problem.
Considering the notably large number of quadratic terms generated from the
tree-shaped constraints, the model is difficult to solve even for small-size
instances. We thus introduce binary decision variables and modify the model
into a nonlinear binary programming problem. In order to solve large-scale RFFA
problems, we outline a simulated annealing algorithm.
