近年來天災發生的頻繁，使得災區的物資配送變得格外重要。因對於傳統仰賴道路狀況的運具反而不易通行。故延伸出的新興運具選擇，如無人機，可以有效配送原先由卡車服務卻因道路損害使得旅行時間增加的需求，此種需求配送的運具選擇替換，提升了整體效率、服務彈性、降低配送成本。
本研究採用具無人機和卡車的兩階層運輸車輛路徑問題，納入旅行時間變異的不確定性概念，並利用 Gurobi 最佳化軟體以最小化卡車使用數和最短旅行時間為目標，於不同規模的測試範例中，比較考量旅行時間不確定性與未考量旅行時間不確定性之結果。對於大規模範例，由於最佳化軟體無法在合理時間內求解，故本模型採用考量多種鄰域解概念的自適應變鄰域搜索算法以處理之，並和標準 VRP 範例比較本模型求解狀況，細部設定如比較有無硬時間窗的限制、不同種營運模式的比較等，並透過模擬分析評估旅行時間變異對於整體配送成本及服務可靠度之影響，進而提出合適之物流系統規劃與營運模式。
結果顯示，相比於不考慮旅行時間變異的確定解，穩健解中總旅行時間普遍上升，因道路損害使得無法於硬時間窗內服務，故增加了旅行時間。而穩健解中卡車距離下降、無人機的距離則增加，穩健解平均的總行駛距離普遍也比確定解長，因加派無人機的緣故，雖然可讓原先卡車旅行時間延長的路段交由無人機服務；相對地，無人機包含發射、回收勢必增加總行駛距離。另一項結果表明，當前如產生無法於硬時間窗內服務的點，首先加派卡車協助直到所有需求被服務完畢，最後如能透過無人機降低旅行時間，才取代之。分析結果表明本研究具卡車和無人機模型可應用於各種配送情境，未來可延伸本模型加入真實路網，以運用於實務中考量不確定因素的層面，作為決策多種運具協作模式之參考。

In recent years, the frequent occurrence of natural disasters has made the distribution of goods in disaster areas particularly important. Because it is not easy to pass by means of transport that rely on road conditions. Therefore, the extended options of emerging transport vehicles, such as drones, can effectively deliver the demand that was originally served by trucks but increased travel time due to road damage. We adopt a two-echelon vehicle routing problem with trucks and drones, incorporate the concept of travel time variation, and use Gurobi to minimize truck usage and travel time. In large-scale problems, we compare robust solution with time uncertainty and deterministic solution without time uncertainty. Since traditional method cannot obtain the optimal solution in a reasonable time, we adopt an adaptive variable neighborhood search that considers various neighborhood solutions to deal with it. Detailed settings such as comparing whether there is a hard time window limit, different operating modes, etc. The results show that, the total travel time in the robust solution generally increases compared with the deterministic solution due to road damage that makes it impossible to serve within the hard time window. In the robust solution, the distance of truck decreases and drone increases, and the average total distance of robust solution is generally longer than that of deterministic solution. In contrast, the launch and recovery of drone will inevitably increase the total distance. In the future, this model can be extended to add the real road network, so as to be applied to the aspect of considering uncertain factors in practice, as a reference for decision-making of multiple vehicle cooperation modes.

Abdulkader, M.M.S., Gajpal, Y., & Elmekkawy, T.Y. (2018). Vehicle routing problem in omni-channel retailing distribution systems. International Journal of Production Economics, 196, 43–55.
Anand, R., Aggarwal, D., & Kumar, V. (2017). A comparative analysis of optimization solvers. Journal of Statistics and Management Systems, 20(4), 623-635.
Bamburry, D. (2015). Drones: designed for product delivery. Design Management Review, 26, 40-48.
Bianchesini, N., & Righini, G. (2005). Heuristic algorithms for the vehicle routing problems with simultaneous pick-up and delivery. Computers and Operations Research, 32, 578-594.
Bonabeau, E. (2002). Agent-based modeling: Methods and techniques for simulating human systems. Proceedings of the national academy of sciences, 99(suppl 3), 7280-7287.
Boysen, N., Schwerdfeger, S., & Weidinger, F. (2018). Scheduling last-mile deliveries with truck-based autonomous robots. European Journal of Operational Research, 271, 1085-1099.
Braaten, S., Gjonnes, O., Hvattum, L. M., & Tirado, G. (2017). Heuristics for the robust vehicle routing problem with time windows. Expert Systems with Applications, 77(1), 136-147.
Bruni, M. E., Beraldi, P., & Khodaparasti, S. (2018). A fast heuristic for routing in post-disaster humanitarian relief logistics. Transportation Research Procedia, 30, 304-313.
Cheng, C., Adulyasak, Y., & Rousseau, L. M. (2018). Formulations and Exact Algorithms for Drone Routing Problem. (working paper).
Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6, 80-91.
Drexl, M. (2012). Synchronization in vehicle routing – a survey of VRPs with multiple synchronization constraints. Transportation Science, 46(3), 297–316.
Faiz, T. I., Vogiatzis, C., & Noor, Md. (2021). Two-echelon vehicle and UAV routing for post-disaster humanitarian operations with uncertain demand. (working paper).
Goksal, F. P., Karaoglan, I., & Altiparmak, F. (2013). A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery. Computers and Industrial Engineering, 65, 39-53.
Han, J., Lee, C., & Park, S. (2013). A robust scenario approach for the vehicle routing problem with uncertain travel times. Transportation Science, 48(3), 373-390.
Hu, C., Lu, J., & Zhang, G. (2018). Robust vehicle routing problem with hard time windows under demand and travel time uncertainty. Computers and Operations Research, 94, 139-153.
Joshi, S., & Kaur, S. (2015). Nearest Neighbor Insertion Algorithm for Solving Capacitated Vehicle Routing Problem. Paper presented at the 2015 IEEE 2nd International Conference on Computing for Sustainable Global Development (INDIACom).
Kitjacharoenchai, P., Min, B. -C., & Lee, S. (2019). Two echelon vehicle routing problem with drones in last mile delivery. International Journal of Production Economics, 225, 1-14.
Kuo, R. J., Lu, S. -H., Lai, P. -Y., & Mara, S. T. W. (2022). Vehicle routing problem with drones considering time windows. Expert Systems With Applications, 191, 1-19.
Li, Y., & Chung, S. (2019). Disaster relief routing under uncertainty: a robust optimization approach. IISE Transactions, 51(3), 869-886.
Martins, L. C., Hirsch, P., & June, A. A. (2020). Agile optimization of a two-echelon vehicle routing problem with pickup and delivery. International Transactions in Operational Research, 28, 1-21.
Murray, C. C., & Chu, A. G. (2015). The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery. Transportation Research Part C, 54, 86-109.
Oruc, B. E., & Kara, B. Y. (2018). Post-disaster assessment routing problem. Transportation Research Part B, 116, 76-102.
Psaraftis, H. N. (1980). A Dynamic Programming Solution to the Single Vehicle Many-to-Many Immediate Request Dial-a-Ride Problem. Transportation Science, 14(2), 130-154.
Pugliese, L. D. P., & Guerriero, F. (2017). Last-mile deliveries by using drones and classical vehicles. International Conference on Optimization and Decision Science, 217, 557-565.
Rizzoli, A. E., Oliverio, F., Montemanni, R., & Gambardella, L. M. (2007). Ant Colony Optimisation for vehicle routing problems: from theory to applications. Swarm Intelligence, 1(2), 135-151.
Sopha, B. M., Siagian, A., & Asih, A. M. S. (2016). Simulating Dynamic Vehicle Routing Problem using Agent-Based Modeling and Simulation. Paper presented at the 2016 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM).
Soysal, M., Ruwaard, J. M. B., & Bektas, T. (2015). The time-dependent two-echelon capacitated vehicle routing problem with environmental considerations. Production Economics, 164, 366-378.
Stenger, A., Vigo, D., Enz, S., & Schwind, M. (2013). An adaptive variable neighborhood search algorithm for a vehicle routing problem arising in small package shipping. Transportation Science, 47(1), 64-80.
Sukarno, S. A. (2019). Approximation methods to vehicle routing problem for a drone fleet management. Université Polytechnique Hauts-de-France.
Sungur, I., Ordonez, F., & Dessouky, M. A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty. (2008). IIE Transactions, 40(5), 509-523.
Toklu, N. E., Gambardella, L. M., & Montemanni, R. (2014). A multiple ant colony system for a vehicle routing problem with time windows and uncertain travel times. Journal of Traffic and Logistics Engineering, 2(1), 52-58.
Vu, L., Vu, D. M., Ha, M. H., & Nguyen, V. -P. (2021). The two-echelon routing problem with truck and drones. International Transactions in Operational Research, 0, 1-27.
Wang, Z., & Sheu, J. B. (2019). Vehicle routing problem with drones. Transportation Research Part B, 122, 350-364.
Wohlsen, M. (2014). The next thing you missed: Amazon’s delivery drones could work—they just need trucks. Wired: Business, Jun, 10.
Yang, F., Wang, Y., Yuan, W., & Li, J. (2014). A robust VRPHTW model with travel time uncertainty. Journal of Systems Science and Information, 2(4), 289-300.