Allocating CO2 emission to customers on a distribution route

• We used cooperative game theory to share the CO2 emitted in a distribution route.
• We applied five methods to both randomly generated instances and a case study.
• In terms of computation time, the Star method outperforms more advanced methods.
• The Lorenz+ Allocation and EPM+ are the most stable and consistent methods.
• The Nucleolus is recommended if stability and robustness are important criteria.

A logistics service provider often delivers goods to multiple customers on a single distribution route and emits CO2 while doing so. Since customers like to know the carbon footprint of products, they are interested in the amount of CO2 that is emitted as a result of their requested orders. Due to differences in location and order characteristics, it is not straightforward what share of the total emission each customer is responsible for. We consider the problem of allocating CO2 emission to each customer and model this problem as an emission allocation game. We use solution concepts from cooperative game theory to develop four emission allocation methods, and compare them to a fifth method based on common practice, referred to as the Star method. We apply all five allocation methods both to a case study and to randomly generated instances. We evaluate every method in terms of stability, consistency, robustness and computation time. Our computational results show that the Star method is outperformed on stability and robustness by the other allocation methods. In terms of consistency and computation time the Star method performs best, although in terms of consistency it is closely followed by other allocation methods. Finally, computation times are acceptable for all five allocation methods on all instances tested.