The authors study the possibility of alleviating traffic congestion when activities of improvement (such as maintenance or rehabilitation) are executed on a public roadway facility, by exploiting excess road capacity along concurrent tolled roadway facilities operating in a public-private partnership. Increased access to the tolled facility is enabled by reducing or suspending tolls during periods of roadway improvement actions and appropriately compensating the tolled facility concessionaire for expected losses.

On the one hand, the public agency seeks to settle the maintenance schedule, toll price reduction and compensation, minimizing the total costs; on the other hand, the concessionaire seeks an optimal toll setting to maximize revenue, thus accepts or rejects the compensation proposed by the public agency, depending on whether it is greater or not to its lost opportunity to profit. Both stakeholders are beholden to the users, who can select the tolled route or the public one. This results in two bilevel problems – one for the agency, one for the concessionaire – and an iterative solution method is proposed to solve them. The solution of each problem is obtained at a Stackelberg equilibrium.

Each of the two bi-level problems is transformed in a single-level problem by adding optimality conditions. The first one is a nonconvex, mixed integer nonlinear program (MINLP), and the second one is a nonconvex nonlinear program (NLP). Both are solved with the nonlinear solver Artelys Knitro and for both the sequential quadratic programming method is exploited.

Results on a case-study show that carefully scheduling the improvement activities and simultaneously agreeing to reduce toll prices can lead to an 8% decrease in total travel time for users, with reduced costs for the public agency and no reduction in total revenue for the concessionaire.