  We propose a new mechanism to design risk-pooling contracts between operators
to facilitate horizontal cooperation to mitigate those costs and improve
service resilience during disruptions. We formulate a novel two-stage
stochastic multicommodity flow model to determine the cost savings of a
coalition under different disruption scenarios and solve it using L-shaped
method along with sample average approximation. Computational tests of the
L-shaped method against deterministic equivalent method with sample average
approximation are conducted for network instances with up to 64 nodes, 10 OD
pairs, and 1024 scenarios. The results demonstrate that the solution algorithm
only becomes computationally effective for larger size instances (above 128
nodes) and that SAA maintains a close approximation. The proposed model is
applied to a regional multi-operator network in the Randstad area of the
Netherlands, for four operators, 40 origin-destination pairs, and over 1400
links where disruption data is available. Using the proposed method, we
identify stable cost allocations among four operating agencies that could yield
a 66% improvement in overall network performance over not having any
risk-pooling contract in place. Furthermore, the model allows policymakers to
evaluate the sensitivity of any one operator's bargaining power to different
network structures and disruption scenario distributions, as we illustrate for
the HTM operator in Randstad.
