Highlights • Optimal parking pricing with parking permits management in a many-to-one park and ride (P + R) network. • A hybrid management with parking pricing and parking permit to reduce system travel cost. • A mixed integer linear program (MILP) to determine system optimum parking permits distribution. • Comprehensive parking management in response to inadequate parking space.

Abstract This paper investigates optimal parking pricing with parking permit management in a many-to-one park and ride (P + R) network in which each origin is connected to the destination by an auto path, a parallel rail transit path and a P + R path. First, we revisit the parking pricing scheme at P + R parking facility with parking restraint and find that it fails to eliminate extra costs arising from competition for inadequate parking spots. Fortunately, competition for inadequate parking spots can be eliminated by a strategy of parking permits distribution. Then we investigate the optimal number of parking permits distributed to each OD pair in a many-to-one park and ride network. The problem is formulated as a mixed-integer linear program (MILP). However, parking permit management is less efficient than parking pricing at P + R facility when parking provision is sufficient. Therefore, we propose two hybrid management schemes with parking pricing and parking permit to reduce system travel cost. Joint implementation of parking pricing and parking permit not only alleviates the traffic congestion but also eliminates the competition for inadequate parking space. Next, the bi-level programming models are proposed to determine the optimal parking fees at P + R parking facilities in the hybrid management schemes. In the bi-level programming models, the number of parking permits assigned or held by each OD pair is an implicit function with respect to parking fee. A global optimum oriented solution algorithm and simulated annealing algorithm are used to solve the MILP and bi-level programming models respectively. Numerical examples are carried out to show that the hybrid schemes with parking pricing and parking permits are more effective than both pure parking pricing scheme and pure parking permits management scheme.