Rescue network design considering uncertainty and deprivation cost in urban waterlogging disaster relief

This work presents a rescue network design problem involving uncertainty and deprivation cost, in which decisions on pumping station setup and drainage truck location and allocation are considered simultaneously. We formulate the problem as a two-stage nonlinear stochastic programming model that is difficult to solve directly because the objective function contains a nonlinear convex deprivation cost function. To address the nonlinearity in the model, quadratic outer approximation and second-order cone programming approaches are employed. Furthermore, utilizing the characteristic that affected time can take finite discrete values, an exact linearization approach is developed to reformulate the deprivation cost function, which leads to a mixed-integer linear programing reformulation. To solve large-scale reformulation problems, a scenario grouping-based progressive hedging algorithm is proposed. A method of constructing must-link constraints is used with K-means++ to efficiently group scenarios. Moreover, extensive numerical experiments and a real-world case study (of a waterlogging risk zone in Zhengzhou, China) are presented to test the applicability and efficiency of the proposed model and solution approaches. Computational results show that the exact linearization approach is competitive in dealing with the deprivation cost function. The proposed algorithm demonstrates the best computational performance in solving large-scale problems.