Most routing decisions assume that routing costs are modelled as a weighted sum of total distance and time traveled by delivery vehicles. However, this assumption does not apply for logistics operations in cities with significant road grades. We study an extension to the VRP model that plans vehicle routes considering the combined impact of detailed road grade information and vehicle load-weight in fuel consumption cost. We refer to this model as the VRP with Steep Roads (VRP-SR), which is formulated as an integer linear program and solved heuristically. In simulated experiments performed for a mountainous metropolitan region in Chile, we estimate operating cost reductions up to $12.4\%$ when compared to the real cost of a plan disregarding road grade information. In addition, we obtain valuable managerial insights from our routing plans; our planned routes tend to initially use roads with relatively small grades to avoid abrupt altitude changes with a loaded vehicle. Higher altitude changes are planned after the vehicle unloads a significant fraction of its cargo. Also, we identify instances in which it is cheaper to insert an intermediate depot visit to drop off weight and split a feasible route in two subroutes to travel over mountainous areas with a lighter vehicle.

大多数路线决策假设路线成本被建模为运输车辆行驶的总距离和时间的加权总和。但是，该假设不适用于道路等级较高的城市的物流运营。我们研究了 VRP 模型的扩展，该模型考虑了详细道路坡度信息和车辆负载重量对燃料消耗成本的综合影响来规划车辆路线。我们将此模型称为带陡峭道路的 VRP (VRP-SR)，它被制定为整数线性程序并启发式求解。在智利山区大都市区进行的模拟实验中，我们估计运营成本降低了$12.4\%$与不考虑道路等级信息的计划的实际成本相比。此外，我们从路线规划中获得宝贵的管理见解；我们计划的路线最初倾向于使用坡度相对较小的道路，以避免装载车辆时突然高度变化。在车辆卸载大部分货物后，计划进行更高的高度变化。此外，我们确定了插入中间仓库访问以减轻重量并将可行路线分成两条子路线以使用较轻的车辆穿越山区的成本更低的情况。