A location-inventory model for distribution centers in a three-level supply chain under uncertainty

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's feasibility and efficiency.