無人機或UAV(無人駕駛飛行器)是一種不用人工操作即可直接飛行的飛行器，現今許多公司嘗試使用無人機來發展他們的物流系統，預計未來幾年運用無人機來運送貨物將會有顯著的成長。雖然無人機運送的速度已經廣為人知，但是其可行性仍存在疑問，仍需近一步的研究，儘管使用無人機來送貨在經濟上是有利的，但在環境方面的效益仍有待檢驗。
本研究提出無人機之車輛途程問題模型，此模型具有兩個目標，即最小化排程總製造時間和總運輸路線的碳排放量。在此模型中，每輛卡車都配備一架無人機並協助運送貨物，本研究目的是提出具有兩個目標的無人機之車輛途程問題的數學模型，然後用多目標基因演算法求解不同規模的問題，並使用效能指標(hypervolume, spacing)去檢查結果的優良。結果顯示，使用此演算法可以產生較好的效能指標，透過顯著性檢定結果顯示，相比於沒有使用無人機，使用無人機減少排程總製造時間和總運輸路線的碳排放量是有顯著差異的。

Drone or UAV (unmanned aerial vehicles) is an aerial vehicle capable of sustained flight without the need for a human operator onboard. Nowadays, many companies tried to develop their own delivery system with drones and the usage of drones in delivery is expected to grow significantly in the next few years. Although the speediness of the drone delivery is known already, but the feasibility of it is still questioned and still need to be studied further. Even though using drone for delivery is beneficial in economic point of view, the benefit in environmental side still needs to be tested.
In this study, a vehicle routing problem with drone (VRPD) model is proposed with two objectives to minimize the makespan and carbon emission of the delivery route. In this model, each truck is equipped with one drone to do collaboration in delivery. The objectives of this study are to propose the mathematical formulation for the VRPD with two objectives, solve it with the NSGA-II algorithm, and test the proposed algorithm with different-scale problems. Hypervolume and spacing are employed to check the quality of the solutions produced by the algorithm. The result shows that the algorithm can produce quite good result with good hypervolume and spacing values. The benefits of using drone to reduce makespan and carbon emission are tested through significance test. The result shows that the difference when using drone is significant.

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