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：及时将货物运输至客户是经济活动的重要组成部分。然而，负责货物运输的重型柴油卡车在洛杉矶、纽约和旧金山等大都市地区排放了大量温室气体。为促进货运电气化，本文提出电动卡车的路径与充电联合调度（JRC）方案。相关优化问题的目标是最小化运输成本、充电成本和延迟成本。由于道路段组合数量庞大，电动卡车可能采取的充电决策和充电时长组合也极为多样。由此产生的混合整数线性规划问题（MILP）即便在确定性情况下也因组合复杂性而极具挑战性。因此，本文采用分层代理拉格朗日松弛方法，将整体问题分解并协调为复杂度显著降低的卡车子问题。在协调过程中，每个卡车子问题基于充电成本、延迟成本和拉格朗日乘子值独立求解。乘子不仅用于引导和协调卡车，还可作为卡车透明且可解释的决策基础。测试结果表明，即使是小规模实例，使用现成求解器CPLEX在数天求解后仍无法解决。而新方法可在几分钟内获得小规模实例的近优解，并在30分钟内完成大规模实例求解。此外，研究表明：随着电池容量增加，总成本显著降低；随着充电功率提升，所需卡车数量也相应减少。