Bi-Objective Optimization for Sustainable Logistics in the Closed-Loop Inventory Routing Problem

This study proposes a bi-objective optimization model for the inventory routing problem with pickup and delivery (IRP–PD) in a closed-loop supply chain, addressing the growing demand for sustainable logistics solutions. The model simultaneously minimizes transportation costs and inventory costs and enhances driver well-being by incorporating regular rest breaks. The network operates within a circular economy framework, where pallets are both delivered and returned for reuse, contributing to waste reduction. A normalized weighted-sum method is initially used to balance the conflicting objectives. However, since the model cannot efficiently solve large-scale instances, we adopt the NSGA-II metaheuristic to generate a Pareto front, enabling decision-makers to explore trade-offs between objectives. The model is tested on a single instance, and the results demonstrate a promising compromise between economic and social goals.