We consider a multi-stage facility reallocation problems on the real line, where a facility is being moved between time stages based on the locations of $n$ agents . Westudy this problem both in the offline setting and online setting . In the online setting the algorithm does not know these future locations and must decide the location of the facility on astage-per-stage basis . We derive the optimal algorithm in both cases . We also consider a generalisation with multiple facilities andweighted agents, for which we show that the optimum can be computed inpolynomial time for a fixed number of facilities . We propose another strategy-proof mechanism which has a competitive ratio of $(n+3/(n+1)$ for even $n$, which we conjecture to be the bestpossible. We also propose another mechanism which is the bestPossible. For the optimum to computed in polynomialtime for a generalising with multiple

Author(s) : Bart de Keijzer, Dominik Wojtczak

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Keywords : facility - setting - facilities - locations - optimum -

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