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locating+ allocation-inventory \\   Doyen \textbf{Doyen  et al. al.}  \cite{DoyenEtal2011} elaborated elaborate on  necessity of pre- and post-disaster planning in relief humanitarian  logistics of earthquake disaster. They for earthquakes. In their study, they  consider a two-echelon inventory logistics  system, which facilitates the transshipment of the relief items to the demand points. In the top echelon, the relief items are stored in (uncapacitatd) regional rescue centers (RRCs) prior to the incident (e.g.,, (e.g.,  an earthquake). Depending on the severity of the incident, which is realized through a set of probabilistic scenarios, the relief items are transmitted to (capacitate) (capacitated)  local rescue centers (LRCs), where they are delivered to the demand points. Accordingly, the authors suggest a two-stage stochastic facility location model program  for pre-positioning and post-distribution of the relief items. In the first stage, the location of the RRCs and their stock level is determined in pre-disaster phase. In the second stage,i.e., in the post-disaster phase,  the decisions regarding the locations of the LRCs are made and the flows of relief items between echelons are determined for each of the scenarios.   For the objective function, the authors have considered determined. The model seeks  minimization of facilities locating costs, inventory holding costs for RRCs, the necessary transportation costs, and the shortage costs. To solve this problem, the authors have developed a Lagrangian relaxation-based heuristics (LH) equipped with local search algorithm. To apply LH, the inter-relating constraints for the echelons are relaxed and lower and upper bounds are computed accordingly. Next, the solution technique performs iterative local search algorithm to improve the quality of the solution.%Therefor, the relief items firstly stored in RRCs in pre-disaster phase and then are distributed to the demand points through LRCs that are set up in the post-disaster stage. The post disaster stage function as the recourse variable as it incorporated uncertainty by defining scenarios on possible earthquake intensity. In the model, minimization of total facility location, inventory holding at RRCs, transportation at each echelon and demand shortage costs is intended. The authors assumed that RRCs are uncapacitated and the LRCs are capacitated, each LRC/demand point can receive items from a single RRC/LRC. In addition, in the model, demand shortage is captured by imposing high penalty cost. The solution procedure utilized Lagrangian relaxation heuristic (LH) armed with local search algorithm, in which LH applied by relaxing joining constraints of the two echelons to obtain a lower bound and an upper bound is calculated by fixing location variables, then local search algorithm iteratively performed in the neighboring of the solution to further improve it.   %The performance evaluation is carried out on a problems ranging from \{5,10\} RRCs, \{10,20,40\}, \{50, 75, 100, 200, 400, 600, 800\} demand points and two scenario types each of with four scenarios. Computational comparison also is conducted with commercial solvers in term of gap reduction and value of stochastic solution (VSS).   %the experiments shows that the procedure significantly outperforms commercial solvers.