Abstract
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.
Highlights
With the rapid growth of many e-retailers, including Amazon (US), Taobao (China), and Rakuten (Japan), many consumers have embraced online shopping in the past few years. e issues of picking, transporting, and delivering hundreds of millions of parcels turn to be critical in the city logistics system
A two-echelon location routing problem (2E-LRP) has been carefully investigated in designing a peripheral logistics mode. e 2E-LRP network consists of a main depot, many satellites, customers, primary vehicles, and secondary vehicles. e main depot is usually assigned with a large capacity and is located away from customers. e primary vehicles depart from the main depot, head to the satellites to meet the satellites’ demand and return to the main depot. e satellites are typically equipped with a small capacity and are located close to customers. e secondary vehicles depart from the satellites, head to the customers to meet the customers’ demand and return to the satellites (Figure 1). e 2E-LRP is solved by locating satellites, assigning customers and planning routes for primary and secondary vehicles
Considering that the 2E-LRPSPD is a new problem, we cannot use existing results to compare the proposed heuristic’s performance with those of other approaches. us, the proposed heuristic is tested on the 2E-LRP and LRPSPD instances by changing the heuristic. is section presents the results of the computational experiments in three stages. e rst stage evaluates the performance of the multistart hybrid heuristic with path relinking (MHH-path relinking (PR)) in the 2E-LRP instances. e second stage investigates the performance of the MHH-PR in the LRPSPD instances. e last stage
Summary
With the rapid growth of many e-retailers, including Amazon (US), Taobao (China), and Rakuten (Japan), many consumers have embraced online shopping in the past few years. e issues of picking, transporting, and delivering hundreds of millions of parcels turn to be critical in the city logistics system. E 2E-LRP is solved by locating satellites, assigning customers and planning routes for primary and secondary vehicles. E contributions of the present study to the improvement of computational efficiency in solving the 2E-LRPSPD are summarised as follows: (1) development of a three-index mixed integer linear programming; and (2) development of a hybrid heuristic that combines VND and LS and is embedded with the path relinking (PR) strategy proposed by Glover and. In the primary network, the primary vehicle with a large capacity departs from the main depot and returns to the main depot a er completing the pickup and delivery of all opened satellites during the rst-level trip. E 2E-LRPSPD is investigated in this work to determine the locations of satellites by selecting the candidates and trips of vehicles to minimise the total cost in the two-echelon system under the following assumptions.
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