Abstract
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.
Highlights
Introduction for a customer simultaneouslyIn this study, we consider a two-echelon vehicle routingIn recent years, the transportation cost in logistics is increasing rapidly
The experimental results show that our algorithm has a good convergence performance, as we find that most instances are finished due to reaching the maximum number of iterations without improving the best solution
We introduce a two-echelon vehicle routing problem with time windows and simultaneous pickup and delivery (2E-VRPTWSPD)
Summary
2E-VRPTWSPD tries to find an assignment of customers to satellites in the second-echelon stage, and determine the vehicle routes with a minimum total cost in both echelons. Information about the distribution process is shown in the table in the right part, where [ei, li] is the time window, ai is the arrival time at each customer or satellite, si is the service time, and di is the demand on customers or the total demand for customers assigned to the satellites In these two examples, we set τ = 0.1. This routing plan is feasible, and its cost is less than that using two first-echelon vehicles This example shows that for 2E-VRPTW with un-fixed service time, which is more general in real-world, it is reasonable to visit a satellite more than once. Note that the route of FV1p is not influenced, because there is no time constraint for the pickup stage of first-echelon vehicles
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