The timely transportation of goods to customers is an essential component of economic activities. However, heavy-duty diesel trucks that deliver goods contribute significantly to greenhouse gas emissions within many large metropolitan areas, including Los Angeles, New York, and San Francisco. To facilitate freight electrification, this paper proposes joint routing and charging (JRC) scheduling for electric trucks. The objective of the associated optimization problem is to minimize the cost of transportation, charging, and tardiness. As a result of a large number of combinations of road segments, electric trucks can take a large number of combinations of possible charging decisions and charging duration as well. The resulting mixed-integer linear programming problem (MILP) is extremely challenging because of the combinatorial complexity even in the deterministic case. Therefore, a Level-Based Surrogate Lagrangian Relaxation method is employed to decompose and coordinate the overall problem into truck subproblems that are significantly less complex. In the coordination aspect, each truck subproblem is solved independently of other subproblems based on charging cost, tardiness, and the values of Lagrangian multipliers. In addition to serving as a means of guiding and coordinating trucks, multipliers can also serve as a basis for transparent and explanatory decision-making by trucks. Testing results demonstrate that even small instances cannot be solved using the over-the-shelf solver CPLEX after several days of solving. The new method, on the other hand, can obtain near-optimal solutions within a few minutes for small cases, and within 30 minutes for large ones. Furthermore, it has been demonstrated that as battery capacity increases, the total cost decreases significantly; moreover, as the charging power increases, the number of trucks required decreases as well.

翻译：货物及时送达客户是经济活动的重要组成部分。然而，在洛杉矶、纽约和旧金山等许多大都市区域，用于运输货物的重型柴油卡车排放了大量温室气体。为促进货运电动化，本文提出了电动卡车的联合路径与充电（JRC）调度方案。相关优化问题的目标是最小化运输成本、充电成本及延迟成本。由于道路段组合数量庞大，电动卡车在充电决策和充电时长方面同样面临大量可能组合。由此产生的混合整数线性规划问题（MILP）即使在确定性情形下也因组合复杂性而极具挑战性。为此，本文采用基于层级的代理拉格朗日松弛方法，将全局问题分解并协调为复杂度显著降低的卡车子问题。在协调环节，各卡车子问题基于充电成本、延迟成本及拉格朗日乘子值独立求解。乘子不仅可用于引导和协调卡车，还能为卡车的透明化、可解释性决策提供依据。测试结果表明，即使是小规模算例，使用商用求解器CPLEX经数天求解也无法解决；而新方法对小规模算例可在数分钟内获得近优解，对大规模算例可在30分钟内实现。此外，研究表明：随着电池容量增加，总成本显著下降；随着充电功率提升，所需卡车数量亦随之减少。