Optimal design of closed-loop supply chain networks with multifunctional nodes

• Mathematical modeling framework for the optimal design of closed-loop supply chain networks.
• Flexible configuration of the network constituted of generalized/multifunctional nodes.
• Generalized nodes’ location and mission is determined by the optimization procedure.
• Evaluation of the proposed MILP model in a real case study.
• Comparison with mainstream counterpart models revealed superiority in terms of cost.

This paper introduces a general mathematical programming framework that employs an innovative generalized supply chain network (SCN) composition coupled with forward and reverse logistics activities. Generalized echelon will have the ability to produce/distribute all forward materials/products and recover/redistribute simultaneously all the returned which are categorized with respect to their quality zone. The work addresses a multi-product, multi-echelon and multi-period Mixed-Integer Linear Programming (MILP) problem in a closed-loop supply chain network design solved to global optimality using standard branch-and-bound techniques. Further, the model aims to find the optimal structure of the network in order to satisfy market demand with the minimum overall capital and operational cost. Applicability and robustness of the proposed model are illustrated by using a medium real case study from a European consumer goods company whereas its benefits are valued through a comparison with a counterpart model that utilizes the mainstream fixed echelon network structure.