A Novel Multi-Objective Inventory Routing Problem with Backhaul Orders in a Multi-Attribute Multigraph Considering Access Tax ^*

Rural areas face significant logistical challenges, including inadequate infrastructure, safety risks, and high transfer costs. Traditional inventory routing models often overlook these complexities, particularly the need for alternative routes and backhaul integration, where routes include deliveries and pickups. This study introduces a Multi-Objective Inventory Routing Problem in a Multigraph with Backhauls (MO-IRPMGB) and employs the Non-dominated Sorting Genetic Algorithm II (NSGA-II) for optimization, achieving average savings of 7% to 14%.