The optimal delivery route problem for truck–drone delivery is defined as a traveling salesman problem with drone (TSP-D), which has been studied in a wide range of previous literature. However, most of the existing studies ignore truck waiting time at rendezvous points. To fill this gap, this paper builds a mixed integer nonlinear programming model subject to time constraints and route constraints, aiming to minimize the total delivery time. Since the TSP-D is non-deterministic polynomial-time hard (NP-hard), the proposed model is solved by the variable neighborhood tabu search algorithm, where the neighborhood structure is changed by point exchange and link exchange to expand the tabu search range. A delivery network with 1 warehouse and 23 customer points are employed as a case study to verify the effectiveness of the model and algorithm. The 23 customer points are visited by three truck–drones. The results indicate that truck–drone delivery can effectively reduce the total delivery time by 20.1% compared with traditional pure-truck delivery. Sensitivity analysis of different parameters shows that increasing the number of truck–drones can effectively save the total delivery time, but gradually reduce the marginal benefits. Only increasing either the truck speed or drone speed can reduce the total delivery time, but not to the greatest extent. Bilateral increase of truck speed and drone speed can minimize the delivery time. It can clearly be seen that the proposed method can effectively optimize the truck–drone delivery route and improve the delivery efficiency.
Although a wide range of literature has investigated the network-level highway maintenance plans and policies, few of them focused on the maintenance scheduling problem. This study proposes a methodology framework to model and compare two different maintenance scheduling strategies for highway networks, i.e., minimal makespan strategy (MMS) and minimal increased travel delay strategy (MITDS). We formulate MMS as a mixed integer linear programming model subject to the constraints of the quantity of manpower and the worst-first maintenance sequence. A bi-level programming model is proposed to quantify and optimize MITDS. The upper level model determines the optimal scheduling to minimize the increased traffic delays during the maintenance makespan. In the lower level, a modified day-to-day traffic assignment model is put forward to reflect the traffic evolution dynamics by simulating travelers’ route choice behaviors. A simulated annealing algorithm and augmented Lagrange algorithm are employed to solve the two proposed models, respectively. Finally, a numerical example using a highway network is developed. The two proposed strategies are tested considering different traffic demands, numbers of engineering teams, and travelers’ sensitivities to traffic congestion. The experiment results reveal that compared with MMS, MITDS extends makespan by 2 days though, it reduces the total increased travel delays by 4% and both MMS and MITDS can obtain the minimum total increased travel delays when the number of engineering teams is 6. The sensitivity analysis indicates that both the two strategies have the maximum and minimum total increased travel delays when the weight of prediction in travelers’ perception is 0.3 and 0.7, respectively. The proposed framework has the potential to provide reference in implementing highway maintenance activities reasonably.
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