A sustainable-circular citrus closed-loop supply chain configuration: Pareto-based algorithms

Configuration of sustainable supply chains for agricultural products has been a well-known research field recently which is continuing to evolve and grow. It is a complex network design problem, and despite the abundant literature in the field, there are still few models offered to integrate social impacts and environmental effects to support network design decision-making to support the configuration of the citrus supply chain. In this work, the citrus supply chain design problem is investigated by integrating the production, distribution, inventory control, recycling and locational decisions in which the triple bottom lines of sustainability, as well as circularity strategy, are addressed. Accordingly, a novel multi-objective Mixed-Integer Linear Programming (MILP) model is proposed to formulate a multi-period multi-echelon problem to design the sustainable citrus Closed-Loop Supply Chain (CLSC) network. To solve the developed model, the ε-constraint approach is employed in small-sized problems. Furthermore, Strength Pareto Evolutionary Algorithm II (SPEA-II) and Pareto Envelope-based Selection Algorithm II (PESA-II) algorithms are used in medium- and large-sized problems. Taguchi design technique is then utilized to adjust the parameters of the algorithms efficiently. Three well-known assessment metrics and convergence analysis are regarded to test the efficiency of the suggested algorithms. The numerical results demonstrate that the SPEA-II algorithm has a superior efficiency over PESA-II. Moreover, to validate the applicability of the developed methodology, a real case study in Mazandaran/Iran is investigated with the help of a set of sensitivity analyses.