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.

The maximal covering location problem (MCLP) seeks to locate a predefined number of
facilities in order to maximize the number of covered demand points. In a classical sense,
MCLP has three main implicit assumptions: all or nothing coverage, individual coverage, and
fixed coverage radius. By relaxing these assumptions, three classes of modelling formulations
are extended: the gradual cover models, the cooperative cover models, and the variable radius
models. In this paper, we develop a special form of MCLP which combines the characteristics
of gradual cover models, cooperative cover models, and variable radius models. The proposed
problem has many applications such as locating cell phone towers. The model is formulated as
a mixed integer non-linear programming (MINLP). In addition, a simulated annealing
algorithm is used to solve the resulted problem and the performance of the proposed method is
evaluated with a set of randomly generated problems.