Generalized benders decomposition approach for designing a reverse logistics network for unused drugs within a circular economy framework

This research has considered the design of a reverse logistics network to purchase and collect surplus/unused drugs from citizens as a solution to drug recycling and correct waste elimination. Surplus drugs are purchased from citizens for the following reasons: (i) the lack of proper management of drug waste can create potential risks for humans and the environment, and (ii) with technological advancements, the possibility of reusing recycled drugs becomes reasonable. In this respect, reverse logistics is among the most important components of achieving a Circular Economy (CE) for manufacturers. This issue is of great importance in the case of essential drugs announced by the World Health Organization (WHO), especially for poorer countries. The proposed model assumes that citizens sell their surplus drugs to the government voluntarily. Then, these drugs are processed correctly in sorting, recycling, and elimination centers in order to supply the essential drugs required. In this research, the Generalized Benders Decomposition (GBD) method was used in the reverse logistics of drugs. Since Benders Decomposition (BD) has been shown to be an appropriate, robust, and highly efficient method for solving medium- and large-size Mixed-Integer Nonlinear Programming (MINLP) problems, our MINLP was solved using the GBD method. The MINLP model was analyzed and solved by adding integer cuts to the master problem. Furthermore, a new method was proposed to tackle the situation where the existing drug processing centers’ capacity is insufficient and there is a need to add new centers. The results show that the proposed algorithm can solve large-size problems much more efficiently than the CPLEX solver.