We study a location-inventory problem in a three level supply chain network under uncertainty, which leads to risk. The (r,Q) inventory control policy is applied for this problem. Besides, uncertainty exists in different parameters such as procurement, transportation costs, supply, demand and the capacity of different facilities (due to disaster, man-made events and etc). We present a robust optimization model, which concurrently specifies: locations of distribution centers to be opened, inventory control parameters (r,Q), and allocation of supply chain components. The model is formulated as a multi-objective mixed-integer nonlinear programming in order to minimize the expected total cost of such a supply chain network comprising location, procurement, transportation, holding, ordering, and shortage costs. Moreover, we develop an effective solution approach on the basis of multi-objective particle swarm optimization for solving the proposed model. Eventually, computational results of different examples of the problem and sensitivity analysis are exhibited to show the model and algorithm & apos; s feasibility and efficiency.

Integrated supply chain includes different components of order, production and distribution and it plays an important role on reducing the cost of manufacturing system. In this paper, an integrated supply chain in a form of multi-objective decision-making problem is presented. The proposed model of this paper considers different parameters with uncertainty using trapezoid numbers. We first implement a ranking method to covert the fuzzy model into a crisp one and using multi-objective particle swarm optimization, we solve the resulted model. The results are compared with the performance of NSGA-II for some randomly generated problems and the preliminary results indicate that the proposed model of the paper performs better than the alternative method.