Highlights • Optimize a location-routing problem with eco-packages in a state-space-time network. • Propose a two-phase optimization model for green eco-packages’ pickup and delivery. • Design a Lagrangian relaxation-based heuristic algorithm to solve the model. • Explore eco-package route sequences in resource sharing pickup and delivery process. • Study synchronization and cost-effectiveness in transport and service phases.

Abstract Optimization of the green logistics location-routing problem with eco-packages involves solving a two-echelon location-routing problem and the pickup and delivery problem with time windows. The first echelon consists of large eco-package transport, which is modeled by a time-discretized transport-concentrated network flow programming in the resource sharing state–space–time (SST) network. The second echelon focuses on small eco-package pickups and deliveries, established by the cost-minimized synchronization-oriented location routing model that minimizes the total generalized cost, which includes internal transportation cost, value of eco-packages, short-term benefits and environmental externalities. In addition, the Gaussian mixture clustering algorithm is utilized to assign customers to their respective service providers in the pickup and delivery process, and a Clarke–Wright saving method-based non-dominated sorting genetic algorithm II is designed to optimize pickup and delivery routes, and improve their cost-effectiveness and degree of synchronization. Different strategy testing results are used in the service phase as input data to calculate the cost of the transport phase, which is solved through a Lagrangian relaxation approach. The 3D SST network representation innovatively captures the eco-package route sequence and state transition constraints over the shortest path in the pickup and delivery at any given moment of the transport phase. A large-scale logistics network in Chengdu, China, is used to demonstrate the proposed model and algorithm, and undertake sensitivity analysis considering the life cycle of green eco-packages.