Ant Colony Approach for Optimizing a Multi-stage Closed-Loop Supply Chain with a Fixed Transportation Charge

Reverse logistics (RL) network can be adequately planned and implemented to gain additional benefits such as maximizing customer satisfaction and a positive image of the business organization, even though most distribution networks are not equipped with reverse channels to deal with the return of merchandise. Therefore, the main objective of this paper is to develop a new mixed-integer nonlinear programming (MINLP) mathematical model with a single-objective, single-product, multi-stage closed-loop supply chain network design (CLSC ND), considering the fixed transportation charge in the distribution network that has been neglected in the recently published papers in the field of CLSC ND. Since such network design challenges belong to the class of NP-hard problems, an algorithm based on ant colony optimization (ACO) is proposed to design a multi-stage RL network with fixed transportation cost and variable cost for the routes. Four network characteristics of different sizes were designed, and 30 instances were randomly generated for each network characteristic to evaluate the effectiveness of the proposed algorithm. The computational analysis of the results shows the high-quality effectiveness of the proposed ACO algorithm compared with the exact results.