Rahman Khorramfar Deleted File  almost 8 years ago

Commit id: d40c637b293c96d6ebaf7524dbafc3de0a16a6a7

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\section{Humanitarian logistics network design under mixed uncertainty}  Tofighi et al. \cite{TofighiEtal2016} argue about \emph{epistemic uncertainty} of disaster-logistic data. They mention that the parameters used in humanitarian logistic have mixed objective-subjective nature, since some of them are obtained from an expert's estimations. This paradigm motivate them to propose a stochastic two-echelon model fro pre-and post disaster logistic planning with fuzzy parameters. The model involve multiple central warehouses (CWs) and multiple local distribution centers (LDCs), and the problem is to determine location and inventory levels of each CW and LDC in the first stage; as well as distribution plan from CWs to LDCs and from LDCs to affected areas(AAs) for the second stage.   Accordingly, they presented the mathematical model of the problem with considering discrete scenario- based uncertainty on both supply and demand. They consider three objectives: 1) total distribution times, 2) minimizes the maximum weighted travel from a CW to demand point, 3) total cost of unused inventories and weighted unsatisfied demands cost. They argue that firs objective captures egalitarian aspect of relief logistic and two latter objectives cover utilitarian aspects (by prioritizing the AAs).  For solving the multi-objective fuzzy stochastic problem, the authors devise a multi-step procedure based on $\epsilon$-constraint paradigm in which, for each objective of the $\epsilon$-constraint model of the problem, first the single objective problem is dufuzzified, then the stochastic model convert to deterministic model by the method proposed by \cite{BirgeLouveaux2011} and finally the single objective crisp model is solved by tailored differential evolution (DE) algorithm.   For evaluation of the model, a set of small-sized problem are solved by commercial solvers and for a case study on data obtain from Tehran metropolitian area the authors utilized proposed metaheuristic method