Mobility operator service capacity sharing contract design to risk-pool against network disruptions

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.