  The INFORMS RAS 2019 Problem Solving Competition is focused on the integrated
train blocking and shipment path (TBSP) optimization for tonnage-based
operating railways. In nature, the TBSP problem could be viewed as a
multi-commodity network design problem with a double-layer network structure.
By introducing a directed physical railway network and a directed train
services (blocks) network, we formulate completely the TBSP problem as a mixed
integer linear programming (MILP) model that incorporates all decisions,
objectives and constraints especially the merge flow (called intree rule here)
in an integrated manner. The scale of the MILP model can be reduced efficiently
if we only enumerate the arc selection and block sequence variables for each
shipment on the legal paths from its origin to its destination satisfying the
given detour ratio. We further develop a sequential algorithm that decomposes
the TBSP problem into the shipment path subproblem and train blocking
subproblem which are solved sequentially. Computational tests on the three
given data sets show that the reduced MILP model can solve DataSet\_1 to
optimality in 8.48 seconds and DataSet\_2 with a gap of 0.16\% in 6 hours on a
GPU workstation. The reduced model also can provide strong lower bounds for
DataSet\_2 and DataSet\_3. The sequential algorithm can find a high quality
solution with 0.04\% gap within 0.26 seconds for DataSet\_1, 0.42\% gap within
4.53 seconds for DataSet\_2 and 1.54\% gap within 0.58 hours for DataSet\_3
respectively on a Thinkpad laptop.
