A Probabilistic Analysis of the Capacitated Facility Location Problem

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.