Tractable approximations for the distributionally robust conditional vertex p-center problem: Application to the location of high-speed railway emergency rescue stations

This article introduces a variation of the p-center problem (PCP), called distributionally robust conditional vertex p-center problem. This problem differs from the conventional PCP in the sense that (i) some key centers in a given set of candidates are designated, and (ii) a distributionally robust optimization (DRO) method is developed. We present a distributionally robust chance-constrained model to formulate this problem. In terms of tractability, we propose a safe tractable approximation method to reformulate the original DRO model as mixed-integer second-order cone programs under the bounded and Gaussian perturbation ambiguous sets. We further use the branch-and-cut algorithm to solve the tractable counterpart models. The application of the DRO model is illustrated for locating emergency rescue stations in the high-speed railway network by two different sized case studies. Finally, we demonstrate the advantages of the DRO model in comparison with the traditional robust optimisation model and the nominal stochastic programming model.