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\section{The bi-objective stochastic covering tour problem}
Tricoire et al. \cite{TricoireEtal2012} study a variant of the Covering Tour Problem (CTP), which arises in post-disaster humanitarian logistics. After a disaster, its of dire importance to set up distribution center for delivering relief items to population centers(named as village in the paper) . In their network model, there is a main depot that supplies distribution centers and the aim is to select a set of nodes from population centers(affected areas) for locating distribution centers(DCs), but, Unlike traditional CTP, which assume coverage is only for nodes that their distance from a DC is below a certain distance, the authors consider a non-increasing function of distance, allowing percentage of villagers to receive relief items. Morever demands are considered as a random variables, and their distribution is a function of village population and village-specific correction term.
The
problem model have been formulated as a bi-objective two-stage stochastic
program with recourse
action action, which minimizes total costs of DCs' setup and vehicle routing in the first objective and expected unsatisfied demand as the second objective. For tackling the random variable, it is approximated by fixed number of samples scenarios. The problem is then solved by $\epsilon-constraint& method to obtain Pareto front,
The quantities assumed to be In this approach, the given
distribution of the random
variables with a known joint vector x is approximated by an
empirical sample distribution, obtained by drawing N scenarios
xðnÞ ðn ¼ 1, . . . ,NÞ from the original distribution
of x,