Joint implementation of tradable credit and road pricing in public-private partnership networks considering mixed equilibrium behaviors

•Propose joint management schemes with tradable credits and road tolls for PPP networks.•Optimize the hybrid management scheme considering UE-CN mixed behaviors.•Decentralize the system optimum (SO) link flows into a UE-CN mixed equilibrium.•Develop three bi-objective optimization models ensuring the target SO flow pattern.

This paper investigates joint road charging schemes in a public-private partnership (PPP) network by simultaneously taking into account Cournot-Nash (CN) players and user equilibrium (UE) players. Each joint scheme comprises a tradable credit plan for public roads and a regular tolling plan for private roads. We show that, under UE-CN mixed equilibrium, there exist anonymous nonnegative joint schemes that can support a system optimum link flow pattern. By using preemptive approach, we further design three bi-objective optimization models with hybrid implementation of tradable credit and road pricing. Numerical examples demonstrate that the proposed methods are effective in managing PPP networks.