Abstract
The solution value \(Z_n^*\) of a stochastic version of the capacitated facility location problem is studied. It is shown that, for large numbers of customers n, the value of \(\tfrac{1}{n}Z_n^*\) can be closely approximated by θ, where the constant θ is identified as a function of the parameters of the underlying stochastic model. Furthermore, an extensive probabilistic analysis is performed on the difference \(\tfrac{1}{n}Z_n - \theta\) that includes an exponential inequality on the tail distribution, a classification of the speed of convergence and a central limit theorem.
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Piersma, N. A Probabilistic Analysis of the Capacitated Facility Location Problem. Journal of Combinatorial Optimization 3, 31–50 (1999). https://doi.org/10.1023/A:1009861004623
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DOI: https://doi.org/10.1023/A:1009861004623