In this paper, a closed-loop supply chain (CLSC) is modeled to obtain the best location of retailers and allocate them to other utilities. The structure of CLSC includes production centers, retailers’ centers, probabilistic customers, collection, and disposal centers. In this research, two strategies are considered to find the best location for retailers by focusing on 1- the type of expected movement 2- expected coverage (distance and time) for minimizing the costs and maximizing the profit by considering the probabilistic customer and uncertainly demand. First of all, the expected distances between customers and retailers are calculated per movement method. These values are compared with the Maximum expected coverage distance of retailers, which is displayed in algorithm 1 heuristically, and the minimum value is picked. Also, to allocate customers to retailers, considering the customer's movement methods and comparing it with Maximum expected coverage time, which is presented in Algorithm 2 heuristically, the minimum value is chosen to this end, a bi-objective nonlinear programming model is proposed. This model concurrently compares Strategies 1 and 2 to select the best competitor. Based on the chosen strategy, the best allocation is determined by employing two heuristic algorithms, and the locations of the best retailers are determined. As the proposed model is NP-hard, a meta-heuristics (non-dominated sorting genetic) algorithm is employed for the solution process. Afterward, the effectiveness of the proposed model is validated and confirmed, and the obtained results are analyzed. For this purpose, a numerical example is given and solved through the optimization software.