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This study proposes a three-index flow-based mixed integer formulation to solve a two-echelon location routing problem with simultaneous pickup and delivery. In this formulation, pickup and delivery demands can be addressed using the same vehicle in each echelon of the network to reduce costs and increase logistics efficiency. We solve such NP-hard problem by developing a multistart hybrid heuristic with path relinking (MHH-PR) which is composed of local search and a variable neighbourhood descent algorithm. In the algorithm, three constructive heuristics are applied to generate diversified initial solutions, and path relinking is introduced for intensification and postoptimisation. Results indicate that MHH-PR can reduce the gap between the near optimal and global optimal solutions by 1%-2%. The proposed algorithm significantly improves computational efficiency by reducing the computational time of more than 10 min for existing cases involving 20 nodes to less than 10 s.

journal of advanced transportation

Presenting a Multi-Start Hybrid Heuristic for Solving the Problem of Two-Echelon Location-Routing Problem with Simultaneous Pickup and Delivery (2E-LRPSPD)