Optimization of concession period for public private partnership toll roads

In the past decades, public private partnership (PPP) has been widely used as an effective approach to stimulating private investment and improving supplies for public services. The optimization of the concession period is very critical for the successful implementation of PPP projects. This paper takes decision making activities of the concession period as a bargaining game process between public and private sectors, and presents a mathematical model to calculate the optimal concession period under a series of assumptions. Backward induction is applied to solve this optimization problem. Finally, numerical simulation is used to further verify the model and analyze the influence of different factors on the optimal concession period. The results indicate that the optimal toll rate should be determined based on the average level of service provided. Factors such as the risk interest rate, initial investment, reservation utility are positively correlated with the optimal concession period, while the private equity ratio and the toll rate are negatively correlated with it. The current study is a useful supplement to previous research works as it incorporates the influence of public equity and time value of money into the construction of model. Moreover, it can act as a helpful reference for both public and private sectors in negotiations concerning related issues.