The ex-post evaluation of the minimum local reliability level: An enhanced probabilistic location set covering model

In order to evaluate the behavior of three probabilistic location set covering models we propose a new method that allows the ex-post measurement of the so called ‘minimum local reliability level’, both under the independence and under the dependence assumption. We show experimentally, by means of a set of test problems, that the proposed loss-system version of Ball and Lin's model does almost always achieve the required reliability level. Moreover, if we compare this new version with the other two already known probabilistic models and consider as a second additional criterion the least number of required vehicles, we show that the new version has a better behavior both under the independence and the dependence assumption. In this paper we further propose a new model with the aim of reducing the number of required vehicles while satisfying the fixed reliability level. Our new model is formulated like Ball and Lin's model incorporating the servers' workload estimate of the Binomial Location Set-Covering Problem of ReVelle and Hogan. Finally, we check the precision of our ex-post evaluation method over the four considered models through a simulation study.