Impact of dynamic flexible capacity on reverse logistics network design with environmental concerns

In this paper, we propose a multi-objective reverse logistics network design model for multiple periods under uncertainty. The proposed model addresses the conflicting objectives of maximizing profit and minimizing carbon emissions in a reverse logistics network design problem. We conceptualize dynamic flexibility in capacity levels of different facilities in reverse logistics under multi-objective optimization setting. Our dynamic flexible capacity model allows the decision makers to increase or decrease the capacity levels of facilities in different periods. Augmented $$\varepsilon $$ ε -constraint method is considered to solve the multi-objective optimization problem. Our analysis shows that the flexible capacity can improve the profit and reduce the carbon emission when compared with the fixed capacity case. Sensitivity analysis is carried out with respect to different costs and subsidies in the system to illustrate the robustness of the model. The analysis shows that the Pareto-frontiers associated with low cost and high subsidy dominate that of high cost and low subsidy, respectively. Results of the study suggest the need for providing flexible capacity levels in designing the reverse logistics network with environmental concerns for a better performance of reverse logistics.