Vehicle Routing Problem for Emissions Minimization

There is extensive literature related to vehicle emissions, and several laboratory and field methods are available for estimating vehicle emissions rates (1). Research indicates that CO2 is the predominant transportation GHG and is emitted in direct proportion to fuel consumption, with a variation by type of fuel (2). For most vehicles, fuel consumption and the rate of CO2 per mile traveled decrease as vehicle operating speed reaches approximately 55 or 65 mph and then begins to increase again (2); hence, the relationship between emission rates and travel speed is not linear. Congestion has a great impact on vehicle emissions and fuel efficiency. In real driving conditions, there is a rapid nonlinear growth in emissions and fuel consumption as travel speeds fall below 30 mph (3). CO2 emissions double on a per-mile basis when speed drops from 30 mph to 12.5 mph or when speed drops from 12.5 mph to 5 mph. Frequent changes in speed, as in stop-and-go traffic conditions, increase emission rates because fuel consumption is a function of not only speed but also acceleration rates (4). These results were obtained with an emission model and freeway sensor data in California and weighted on the basis of a typical light-duty fleet mix in 2005. The volume of emissions per mile is a function of the speed profile from the departure time until reaching destination. In congested urban areas with significant speed changes due to recurrent congestion, such as predictable low speeds due to capacity constraints at peak hours, departure time must be considered in the design of EVRP routes. The time-dependent VRP (TDVRP) takes into account that links in a network have different costs or speeds during the day. Typically this is used to represent varying traffic conditions. The TDVRP was formulated by Malandraki and Daskin (5). Time-dependent models are significantly more complex and computationally demanding than are static VRP models; recent approaches to solving the TDVRP are reviewed elsewhere (6–8). An up-to-date and extensive TDVRP literature review is presented in another paper (8). TDVRP instances are more data intensive than are static VRP instances, but their solution is likely to achieve environmental benefits in congested areas, albeit in an indirect way because emissions are not directly optimized (9). Other researchers conducted surveys indicating that emissions can be substantially reduced if companies improve the efficiency of routing operations (10, 11). Woensel et al. used queuing theory to model the impact of traffic congestion on emissions Vehicle Routing Problem for Emissions Minimization