Addressing the principal-agent problem in public private partnerships via mixed-integer bi-level linear programming (2020)
Public Private Partnerships (PPPs) are associations between a government and a private party with the objective of delivering public assets and/or services. The private party provides financial leverage and technical expertise to develop large-scale projects, responding to the requirements and conditions specified by the public party, which, in turn, must oversee the adequate development of the project. A key challenge arises due to the Principal-Agent problem (PA problem), namely: a conflict of interests in which the public may not be able to ascertain whether the private party's actions respond to its own interests rather than the project's. The interactions in a PPP can thus be viewed as a Stackelberg Game and consequently as a bi-level optimization problem, in which a leader (the government) and a follower (a private contractor) partake in coupled decision processes, where the follower's decisions depend on previous leader decisions and cause an impact on the leader's objective. We propose a bi-level optimization framework to model PPPs in the context of a road maintenance as a typical example of infrastructure operation projects. The problem under consideration involves integer decision variables, which complicates the solution strategy for bi-level optimization problems. Thus, we incorporate recent Branch & Bound and Branch & Cut methodology approaches found in the operations research literature. The use of MIBLPs allows to model interactions in PPPs (e.g., PA problem), while considering potentially complex combinatorial problems resulting from the project's characteristics (e.g., infrastructure maintenance). Finally, our model can find bi-level feasible maintenance and inspection plans for both parties within reasonable computation times, allowing for analysis of trade-offs in PPPs and potential strategies to overcome drawbacks such as the PA problem