Abstract: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.

Abstract:Maintaining a balance between revenue and expenditure is the key to the sustainable development of a bicycle sharing system (BSS), and is a challenge for almost all systems worldwide. This article proposes a dynamic programming approach to obtain the optimal strategy to maximize the revenue of overall BSS. The Variable Granularity-Depth First Search (VG-DFS) algorithm is designed to speed up the solution. A numerical experiment is presented to verify the applicability of the model through a comparison with real data from the BSS in Hangzhou. Results indicated that the BSS could achieve break-even, or even obtain a substantial income by utilizing our model to make operational decisions, especially when the region it is located in has a relatively high GDP. Moreover, the best investment strategy proved is to involve stations in the initial construction period of the BSS as much as possible.