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Customer returns are a common phenomenon in many industries, and they have a significant impact on business organizations and their supply chains. False failure returns are returned products that have no functional or cosmetic defects, and they represent a large body of customer returns in practice. In this paper, we develop a mixed-integer nonlinear programming model to study a multicommodity location-inventory problem in a forward-reverse logistics network. This model minimizes the total cost in this network by considering false failure returns, and it also considers many real-world business scenarios in forward and reverse logistics flows. Moreover, we design a new heuristic approach to solve the model efficiently. Finally, numerical experiments are conducted to validate our solution approach and provide meaningful managerial insights.