Robust Optimization for the Two-Echelon Crowdsourced Pickup and Delivery Problem with Time Windows under Travel Time Uncertainty

Abstract

This study presents a robust two-echelon crowdsourced pickup and delivery problem with time windows (R2E-CPDPTW) to optimize routing and order allocation between first-echelon vehicles and second-echelon crowdsourced and contracted vehicles under travel time uncertainty. Formulated as a route-based set-partitioning model, it employs a cardinality-constrained uncertainty set to characterize travel time variations and preserve strict temporal synchronization between the two echelons. To solve this complex model to optimality, a customized branch-price-and-cut (BPC) exact algorithm is developed, where the pricing subproblem is solved as a robust shortest path problem with resource constraints. Computational results demonstrate the algorithm’s efficiency in yielding exact solutions and highlight the critical trade-offs between system robustness and operational costs.