The time-dependent pollution-routing problem

• We use a modeling approach for reducing greenhouse gas emissions in a presence of traffic congestion.
• We show that idle waiting can be used as effective strategy to reduce vehicle emissions.
• We present analytical properties based on a single-arc version of the problem.
• We provide insights on the trade-off between emission costs and driver wage.
• We describe a procedure to optimize departure times and travel speeds on a fixed route.

The Time-Dependent Pollution-Routing Problem (TDPRP) consists of routing a fleet of vehicles in order to serve a set of customers and determining the speeds on each leg of the routes. The cost function includes emissions and driver costs, taking into account traffic congestion which, at peak periods, significantly restricts vehicle speeds and increases emissions. We describe an integer linear programming formulation of the TDPRP and provide illustrative examples to motivate the problem and give insights about the tradeoffs it involves. We also provide an analytical characterization of the optimal solutions for a single-arc version of the problem, identifying conditions under which it is optimal to wait idly at certain locations in order to avoid congestion and to reduce the cost of emissions. Building on these analytical results we describe a novel departure time and speed optimization algorithm for the cases when the route is fixed. Finally, using benchmark instances, we present results on the computational performance of the proposed formulation and on the speed optimization procedure.