Vehicle routing problem with steep roads

Abstract 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.