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Rahman Khorramfar edited section_The_bi_objective_stochastic__.tex
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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 model have been formulated as a bi-objective two-stage stochastic program with recourse action, which minimizes total costs of DCs' setup and vehicle routing in the first objective and expected unsatisfied demand as the second objective.
At first stage, open DCs and tour of vehicle for visiting DCs are determined, and at the second stage as problem realized(during delivery period), based on the information gathered from DCs, the driver decide actual deliveries to each DC on each tour.
For tackling the random variable,
it distribution of demands is approximated by fixed number of
samples sample scenarios.
To obtain Pareto solutions, The problem is
then solved by
a heuristic, based $\epsilon$-constraint
method to obtain method. The algorithm incorporates branch-and -cut algorithm for eliminating sub-tours at DC nodes. In their computational study, exact Pareto
front, solution of real data gathered from rural communities in Senegal is presented.