Orateur
Description
The problem of pricing mobility services has attracted significant attention. In most studies, uncertain demand is modeled as an exogenous random variable with known distribution. This assumption overlooks the likely effect of prices on user adoption decisions. To address this dependency, we formulate the pricing problem as a stochastic program with decision-dependent demand uncertainty. Specifically, we make the non-standard assumption that the distribution of demand depends on pricing decisions. We show that the problem can be written as an extensive mixed-integer linear program whose size is exponential in the input parameters. To find numerical solutions we devise a specialized exact decomposition method. The method builds on distribution-specific cuts for the generation of which we prove closed-form primal and dual solutions to the necessary sub-problems. Extensive numerical experiments on a one-way carsharing system operating in Copenhagen, Denmark, demonstrate that taking into account the effect of prices on uncertain demand increases the expected profits by 4.91% compared to a benchmark considering deterministic price-elastic demand. Service rates are likewise high, corresponding to 93.37% on expectation. Furthermore, we show that the solution method outperforms by far a commercial solver used to solve the monolithic formulation, hereby extending the domain of practically tractable problems. While the focus of the paper is on carsharing services, we comment on how the proposed modeling and solution strategy naturally extends to many types of mobility pricing problems.
