Development of supply chains is one of the practical concepts in the field of production and sales in competitive conditions. Accordingly, it is necessary to properly study the competitive conditions in which supply chain networks can be designed. In this regard, the present research contributes to the field by incorporating the market share and customer satisfaction to the competitive conditions of supply chains. For this purpose, a nonlinear mathematical model is presented in order to find locations and perform distributions in a closed-loop supply chain under competitive conditions. This model has two objectives including profit maximization and market share maximization. To solve the model, LP-metric and goal programming are implemented, and then the results of these two methods are discussed. Comparisons are also made in terms of the value of the objective functions as well as the solution time. Finally, the simple weighted sum method is used to select the superior method. The results show that the LP-metric method is worth performing to solve the mathematical model of the research.
