A rolling horizon approach for multi-objective optimization of two-way logistics with postponed orders

Abstract

Last-mile delivery of e-commerce is a complex mix of simultaneous delivery of goods and pickup of returned goods. With return rates being substantial in the e-commerce sector, this problem is highly relevant. To address this challenge, this study formulates a rolling horizon simultaneous pickup and delivery problem with time windows in a two-way logistics system. The proposed approach integrates a multi-objective mixed-integer linear programming model with a rolling-horizon framework, allowing forward deliveries and reverse pickups to be postponed based on different priorities and penalties, while capturing the interdependence between outbound and return flows. Economic efficiency, environmental impact, and social factors are explicitly incorporated into the objective function. For large-scale instances, an adaptive large neighborhood search with simulated annealing metaheuristic is designed and compared against a weighted-sum mixed integer linear program approach. Numerical experiments on Solomon datasets demonstrate that the proposed method efficiently achieves high-quality solutions, reveals trade-offs among sustainability objectives, and shows how coordinating forward and reverse flows can enhance operational adaptability. The results also highlight an unintended outcome of the proposed rolling-horizon planning: generation and propagation of backlog of demand. This highlights the need for adaptive mechanisms that can manage such issues in multi-period planning.