Distributionally robust optimization for collaborative emergency response network design

The post-disaster emergency response capacity of a single country is limited, and a collaborative approach that pools emergency resources can improve disaster resilience. In this paper, we study a multi-country collaborative emergency response network design problem with uncertain demand and transportation time. Considering the benefits of inter-regional cooperation in sharing emergency facilities and resources, we construct a collaborative emergency response network (CERN) design framework. The cost of CERN is allocated among the partner countries according to their expect standalone response cost and the level of economic development. In practice, the distribution information of random parameters is not perfectly known, so we propose a distributionally robust optimization (DRO) model to design the CERN. A scenario-wise ambiguity set is constructed to characterize the uncertain parameters based on disaster-level-related events. To solve the proposed DRO model, we propose a decomposition-based algorithm with a valid inequality. In the numerical study, we first verify the advantage of the CERN design approach. The proposed scenario-wise DRO method is subsequently compared with alternative modeling approaches to assess its out-of-sample performance. The findings confirm the efficacy of the constructed ambiguity set in capturing the uncertainty stemming from varying magnitudes of catastrophic events. The computational study demonstrates that the proposed algorithm exhibits superior computational efficiency compared to the commercial solver CPLEX for large-scale problems. Additionally, we conduct sensitivity analyses on various parameter configurations and provide managerial insights for the CERN design problem.