Green Routing Game: Strategic Logistical Planning using Mixed Fleets of ICEVs and EVs

TL;DR

This paper models a strategic routing game for logistics operators with mixed fleets of ICEVs and EVs, analyzing equilibrium conditions and trade-offs between pollution and delay costs.

Contribution

It introduces a novel green routing game framework with mixed vehicle fleets, characterizes Nash equilibria, and proposes a distributed computation method.

Findings

Higher pollution costs reduce equilibrium inefficiency

Charging congestion impacts EV routing decisions

Trade-offs between delay and pollution costs are quantifiable

Abstract

This paper introduces a "green" routing game between multiple logistic operators (players), each owning a mixed fleet of internal combustion engine vehicle (ICEV) and electric vehicle (EV) trucks. Each player faces the cost of delayed delivery (due to charging requirements of EVs) and a pollution cost levied on the ICEVs. This cost structure models: 1) limited battery capacity of EVs and their charging requirement; 2) shared nature of charging facilities; 3) pollution cost levied by regulatory agency on the use of ICEVs. We characterize Nash equilibria of this game and derive a condition for its uniqueness. We also use the gradient projection method to compute this equilibrium in a distributed manner. Our equilibrium analysis is useful to analyze the trade-off faced by players in incurring higher delay due to congestion at charging locations when the share of EVs increases versus a higher pollution cost when the share of ICEVs increases. A numerical example suggests that to increase marginal pollution cost can dramatically reduce inefficiency of equilibria.