Balancing public and private interests through optimization of concession agreement design for user-pay PPP projects

In user-pay public private partnership (PPP) projects, private sectors collect user fees to cover cost and reap revenue. For projects that cannot be self-financed, public sectors usually invest public funds to make them financially feasible. The concession agreement allocates revenues and risks, and lies in the center of balancing public and private interests. However, stakeholders may have contrary opinions regarding the optimization of concession agreement. While private sectors are concerned about earning money, public sectors pay more attention to the efficient use of public funds. To address this challenge, this paper firstly identifies several key concessionary items, including concession period, concession price, capital structure and government subsidy. Then, a multi-objective optimization model is presented using discounted cash flow method, in which key concessionary items act as decision variables and public and private interests are represented by two sub-objectives. Subsequently, the model is solved using non-dominated sorting genetic algorithm-II (NSGA-II). Furthermore, a numerical case based on Beijing No. 4 Metro Line is provided to demonstrate the application of the model. Results show that the proposed model can produce a series of viable combinations of concessionary items that balance public and private interests, which provides practical references for relative decision making activities.