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On the Power of Static Assignment Policies for Robust Facility Location Problems

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Integer Programming and Combinatorial Optimization (IPCO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12707))

Abstract

We consider a two-stage robust facility location problem on a metric under an uncertain demand. The decision-maker needs to decide on the (integral) units of supply for each facility in the first stage to satisfy an uncertain second-stage demand, such that the sum of first stage supply cost and the worst-case cost of satisfying the second-stage demand over all scenarios is minimized. The second-stage decisions are only assignment decisions without the possibility of adding recourse supply capacity. This makes our model different from existing work on two-stage robust facility location and set covering problems. We consider an implicit model of uncertainty with an exponential number of demand scenarios specified by an upper bound k on the number of second-stage clients. In an optimal solution, the second-stage assignment decisions depend on the scenario; surprisingly, we show that restricting to a fixed (static) fractional assignment for each potential client irrespective of the scenario gives us an \(O(\log k/\log \log k)\)-approximation for the problem. Moreover, the best such static assignment can be computed efficiently giving us the desired guarantee.

V. Goyal—Supported in part by NSF CMMI 1636046.

D. Shmoys—Supported by CCF-1526067, CMMI-1537394, CCF-1522054, CCF-1740822, CCF-1526067, CNS-1952063, and DMS-1839346.

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Correspondence to Omar El Housni .

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El Housni, O., Goyal, V., Shmoys, D. (2021). On the Power of Static Assignment Policies for Robust Facility Location Problems. In: Singh, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2021. Lecture Notes in Computer Science(), vol 12707. Springer, Cham. https://doi.org/10.1007/978-3-030-73879-2_18

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  • DOI: https://doi.org/10.1007/978-3-030-73879-2_18

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