Mathematical modeling of CO2e emissions in one-to-one pickup and delivery problems

The road freight transportation sector is a significant emitter of carbon dioxide equivalents (CO₂e), which are directly proportional to fuel consumption. Multi-vehicle, multi-depot one-to-one pickup and delivery pollution-routing problem (PDPRP) is an extension of the classical vehicle routing problem with time windows (PDVRPTW) which consists of routing a number of vehicles to serve a set of customers and deciding on their speed on each route so as to minimize a total function comprising fuel and driver costs. A mathematical model of the one-to-one PDPRP is non-linear in nature, although it can be linearized and represented as a mixed integer linear programming formulation. Computational results show the importance of using fuel consumption objective instead of distance- or time-based cost functions.