電動卡車與機器人協同配送之路徑優化問題

The Optimal Routing Problem of Electric Truck-Robot Collaborative Distribution

本研究以物流業者的角度，針對電動卡車與機器人協同配送之車輛路線問題提出數學模式與演算法。模式以混合整數線性規劃建構，考量顧客時間窗、電動卡車充電需求及機器人電量管理，並允許兩者同步進行配送作業以降低總配送成本。本研究利用Gurobi求解小規模問題，可在20分鐘內獲得最佳解。然而，車輛路線問題屬NP-hard，大規模問題情境下Gurobi無法在合理時間內求得最佳解，因此提出模擬退火法（Simulated Annealing, SA）與變動鄰域搜尋法（Variable Neighborhood Search, VNS）測試結果顯示，SA與VNS均能於短時間內求得高品質解，平均表現優於Gurobi，具實務應用潛力。本研究除填補電動卡車與機器人協同配送在電量管理與時間窗限制等研究缺口外，亦可為物流業者推動永續配送提供理論與實務貢獻。

This study develops a mathematical model and algorithms for the vehicle routing problem of collaborative delivery with electric trucks and robots from the perspective of logistics providers. The model is formulated as a mixed-integer linear program, incorporating customer time windows, charging requirements of electric trucks, and battery management of robots, while allowing simultaneous delivery operations to minimize the total distribution cost. Small-scale instances are solved using Gurobi, which can obtain optimal solutions within 20 minutes. However, since the vehicle routing problem is NP-hard, Gurobi fails to find optimal solutions within a reasonable runtime for large-scale instances. To address this, two metaheuristics—Simulated Annealing (SA) and Variable Neighborhood Search (VNS)—are proposed. Experimental results indicate that both SA and VNS can efficiently produce highquality solutions within a short time, with average performance superior to Gurobi, demonstrating strong potential for practical applications. Beyond addressing research gaps in energy management and time window constraints for electric truck–robot collaboration, this study also provides theoretical and practical contributions to support logistics providers in advancing sustainable delivery.