An optimization model with a lagrangian relaxation algorithm for artificial internet of things-enabled sustainable circular supply chain networks

Circular supply chain (CSC) networks improve sustainability and create socially responsible enterprises through recycling, harvesting, and refurbishing. This study develops a Lagrangian relaxation (LR) algorithm for solving location-inventory-routing (LIR) problems with heterogeneous vehicles in multi-period and multi-product sustainable CSC networks. The proposed Artificial Internet of Things (AIoT) enabled sustainable CSC is designed to increase network performance and create a secure and traceable environment. For the first time, an LR algorithm is proposed to solve the LIR problems in an AIoT-enabled CSC network with storage, backorder shortage, split-delivery, and time window potentials. Sixteen small- and medium-size simulated problems were produced to assess the performance of the proposed algorithm relative to the GAMS software. The results show the proposed algorithm can solve the small- and medium-size problems as effectively as GAMS software but faster and more efficiently. In addition, eight large-size simulation problems were produced and solved by the algorithm. While the GAMS software failed to solve the large-size problems, the LR algorithm solved them efficiently and successfully.