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This paper considers a location-inventory problem in the three-level supply chain where demand across the retailers is assumed to be correlated and inventory shortages are allowed. For better monitoring the stock status, a periodic review of inventory level is taken into account. In order to overcome the joint location-inventory problem, this paper proposes an optimization model based on a mixed integer non-linear programming (MINLP) whose objective function is the minimization of the total supply chain costs. To solve the designed MINLP model, two meta-heuristic algorithms are presented, including genetic algorithm (GA) and simulated annealing (SA) with an appropriate decoding scheme. Since the performance of meta-heuristic algorithms depends on setting the parameters; therefore, the Taguchi method is used to set parameters of the developed solving algorithms. Finally, the proposed algorithms have …