Vehicle routing to minimize time-dependent emissions in urban areas

•We investigate the impact of varying travel speeds and loads on emissions.•We propose a way of keeping the load and time-dependent VRP tractable.•We analyze how the structure of routes changes following varying speeds and loads.•Comparison with traditional objectives shows the trade-off between emissions and costs. This paper focuses on the problem of minimizing CO2 emissions in the routing of vehicles in urban areas. While many authors have realized the importance of speed in minimizing emissions, most of the existing literature assumes that vehicles can travel at the emissions-minimizing speed on each arc in the road network. In urban areas, vehicles must travel at the speed of traffic, which is variable and time-dependent. The best routes also depend on the vehicle load. To solve the problem, we take advantage of previous work that transforms the stochastic shortest path subproblems into deterministic problems. While in general, these paths must be computed for each combination of start time and load, we introduce a result that identifies when the emissions-minimizing path between customers is the same for all loads. When this occurs, we can precompute the paths and store them in a lookup table which saves on runtime. To solve the routing problem, we adapt an existing tabu search algorithm. We test our approach on instances from a real road network dataset and 230 million speed observations. Experiments with different numbers of vehicles, vehicle weights, and pickup quantities demonstrate the value of our approach. We show that large savings in emissions can occur particularly in the suburbs, with heavier vehicles, and with heterogeneous pickup quantities as compared with routes created with more traditional objectives. We show that the savings in emissions are proportionally larger than the associated increases in duration, indicating improved emissions are achievable at a fairly low cost.