A distributionally robust chance-constrained model for humanitarian relief network design

We propose a novel two-stage distributionally robust joint chance-constrained (DRJCC) model to design a resilient humanitarian relief network with uncertainties in demand and unit allocation cost of relief items in the post-disaster environment. This model determines the locations of the supply facilities with pre-positioning inventory levels and the transportation plans. We investigate the problem under two types of ambiguity sets: moment-based ambiguity and Wasserstein ambiguity. For moment-based ambiguity, we reformulate the problem into a mixed-integer conic program and solve it via a sequential optimization procedure by optimizing scaling parameters iteratively. For Wasserstein ambiguity, we reformulate the problem into a mixed-integer linear program. We conduct comprehensive numerical experiments to assess the computational efficiency of the proposed reformulation and algorithmic framework, and evaluate the reliability of the generated network by the proposed model. Through a case study in the Gulf Coast area, we demonstrate that the DRJCC model under Wasserstein ambiguity achieves a better trade-off between cost and network reliability in out-of-sample tests than the moment-based DRJCC model and the classical stochastic programming model.