Design and Control of Public-Service Contracts and an Application to Public Transportation Systems

Until the end of the 20th century it was common that cities organized, financed and managed their own public transportation systems. More recently—in Italy mainly during the last decade—many countries liberalized the service provision of public transportation. Indeed, while o↵ering local public transportation is a political and financial duty of governments, the service provision is outsourced to a private Operator, while the government retains a control position, given to a regulatory Agency. This is a common scheme not only in transportation. In close collaboration with the public transportation agency of the city of Bologna, Italy, we designed a methodology to optimize some aspects of the contractual relationship between that Agency and the bus Operator. We focus on the fines specified by the contract when the Operator fails to comply with the service level it has agreed to provide, and on a procedure to measure that service level. Our approach has the benefit that it aligns the incentives of both parties in the benefit of bus riders. We model the Agency-Operator relationship as a multi-stage game and find its equilibrium to establish the best operating regime. The game theoretic approach provides expressions for the fines that the Operator should be charged if it does not satisfy the contracted services, and for the optimal Agency’s budget to devote to control activities. Second, to check the compliance of the Operator to the schedule specified by the contract in a resource e cient way, we compute how to position the Agency’s employees to verify if buses are running according to the specification in the contract. This is achieved by counting bus services and checking other quality indicators. We formulate this NP-hard problem as a Mixed Integer Linear Program, and propose an algorithm to solve it that is e↵ective in providing itineraries for the controllers working for the Agency.