An equilibrium approach for compensating public–private partnership concessionaires for reduced tolls during roadway maintenance

This study considers the possibility of exploiting excess capacity along concurrent tolled roadway facilities operating in a public–private partnership for the purpose of alleviating traffic congestion during improvement action execution on a public roadway facility. Increased access to the tolled facility is enabled by reducing or suspending tolls during periods of roadway improvement action and appropriately compensating the tolled facility concessionaire for expected losses. The problem of determining an optimal reduced toll pricing strategy and compensation level is referred to as the Maintenance Timing and Price Discovery (MTPD) problem. A multi-level optimization model and iterative solution method are proposed to solve this problem. As toll prices often depend on traffic levels, the model also determines the optimal timing and time-of-day and day-of-week for executing the set of required improvement actions over the planning horizon to ensure a lowest total cost. The multi-level model consists of two bilevel models. Solution of the greater model is attained at a Stackelberg equilibrium between these two bilevel models. An additional Stackelberg equilibrium is sought between upper and lower levels of each of these two bilevel models individually. The MTPD formulation and general solution methodology are applied on an illustrative example from which computational results are obtained. Insights from the results show that this strategy for alleviating traffic congestion during roadway maintenance or other improvement activities can lead to substantial savings in total agency and user costs.