Two-echelon vehicle routing problem with time windows and simultaneous pickup and delivery

This paper proposes a tabu search algorithm for the two-echelon vehicle routing problem with time windows and simultaneous pickup and delivery (2E-VRPTWSPD), which is a new variant of the two-echelon vehicle routing problem. 2E-VRPTWSPD involves three stages of routing: (1) the first-echelon vehicles start from the depot to deliver cargoes to satellites; (2) the second-echelon vehicles start from satellites to serve customers within time windows in a simultaneously pickup and delivery manner and finally return to their satellites with pickup cargoes; (3) the first-echelon vehicles start from the depot to collect cargoes on satellites. To solve this problem, we formulate it with a mathematical model. Then, we implement a variable neighborhood tabu search algorithm with a tailored solution representation to solve large-scale instances. Dummy satellites time windows are applied in our algorithm to speed up the search. Finally, we generate two benchmark instance sets to analyze the performance of our algorithm. Computational results show that our algorithm can obtain the optimal results for 10 out of 11 small-scale instances and produce promising solutions for 200-customer instances within a few minutes. Additional experiments indicate that the usage of dummy satellite time windows can save 19% computation time on average.