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.

翻译：我们提出了一种新机制，用于设计运营商之间的风险池化合同，以促进横向合作，降低中断期间的损失并提升服务韧性。我们构建了一个新颖的两阶段随机多商品流模型，用于确定不同中断情景下联盟的成本节约效果，并采用L型方法结合样本平均近似进行求解。针对最多包含64个节点、10个OD对和1024种情景的网络实例，我们将L型方法与结合样本平均近似的确定性等价方法进行了计算对比测试。结果表明，该求解算法仅在大规模实例（超过128个节点）中才具备计算有效性，且样本平均近似保持了良好的逼近精度。我们将所提模型应用于荷兰兰斯塔德地区一个拥有四家运营商、40个起讫点对及超过1400条链路、且具备可用中断数据的区域多运营商网络。通过所提方法，我们识别出四家运营机构之间的稳定成本分配方案，该方案可使整体网络性能相比无任何风险池化合同的情况提升66%。此外，该模型允许政策制定者评估任一运营商的议价能力对不同网络结构及中断情景分布的敏感性——我们以兰斯塔德地区的HTM运营商为例进行了说明。