Optimal bike allocations in a competitive bike sharing market

This paper studies the bike allocation problem in a competitive bike sharing market. To overcome computational challenges, a continuum approximation (CA) approach is applied, where the allocation points and user demand are assumed to be continuously distributed in a two-dimensional region. Companies offering bike sharing service bear both allocation cost and bike depreciation cost while earning revenue from fare collection. The user's selection of bike service is affected by both walking distance and preference towards bike quality. The elasticity of the demand is considered in relation to the density of allocation points in the market. A leader-follower Stackelberg competition model is developed to derive the optimal allocation strategy for market leader. Two sets of numerical studies - one hypothetical case and one from a real case - are conducted to specify the impact of the parameters on model performance and illustrate how the proposed model can be applied to support the decision making.