Abstract
In this paper, we introduce a model of distributionally robust facility location problem (DRFLP) under moment constraints up to the second order. We show, via duality theory of moment problems, that the linear relaxation of the DRFLP is equivalent to that of the standard uncapacitated facility location problem (UFLP). Consequently, any LP-based approximation algorithm for the UFLP implies an approximation algorithm for the DRFLP with the same approximation ratio.
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Wu, C., Du, D., & Xu, D. (2015). An approximation algorithm for the two-stage distributionally robust facility location problem. In Springer Proceedings in Mathematics and Statistics (Vol. 95, pp. 99–107). Springer New York LLC. https://doi.org/10.1007/978-3-319-08377-3_11
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