Bidirectional Incentive Model for Bicycle Redistribution of a Bicycle Sharing System during Rush Hour

Redistribution is an important part of operational activities in a bicycle sharing system (BSS). This paper proposes that there are two types of users in a BSS: leisure travelers and commuters. The operators and the government are adopting the bidirectional incentive model (BIM) to improve their service level of redistribution. That is, the BIM stimulates leisure travelers to actively respond to bicycle resetting needs of the system; on the other hand, it guides commuters by encouraging them to avoid travelling in peak periods. This is beneficial to achieve the goals of reducing the scheduling pressure on bicycles during rush hour, and even to realize the self-resetting of the BSS. In this paper, we explore three scenarios for implementing BIM through cooperation between the operator and the government. By exploiting Stackelberg games in all models, we illustrate the quantity of users in three different travel behaviors, and surplus value of these users respectively. We also consider the trend of the profit of the operator and the government when some changes of parameters are made. The numerical analysis and case discussion find that the strategy of the operator implementing BIM with a subsidy is the best method for developed regions. In a developing region, the strategy of implementing the BIM with a direct government subsidy to users is the best choice in a small or tourist city. In these cities, the proportion of leisure travelers is always larger than 50%, resulting in a significant incentive effect. The strategy of the operator implementing BIM without a subsidy is the best choice for the large and medium-sized city.