Strategic heterogeneous customers in a transportation station: information and pricing

Abstract

Problem definition: We consider pricing of services with strategic customers who have heterogeneous delay costs motivated by transportation systems. Customers are strategic decision makers who weigh the reward from the transport service against the waiting cost for the vehicle at a transportation station. Customers arrive at the station according to a Poisson process, and the vehicle visits the station according to a renewal process. We analyze the optimal price and the equilibrium for different levels of information available to customers. Methodology/results: We represent the service system as a stochastic clearing process, heterogeneity in delay cost as a random variable, and heterogeneity in rewards as a positive affine transformation of delay cost. For each information level, we identify the equilibrium behavior of customers and solve the revenue-maximization problem based on this equilibrium. The equilibrium turns out to be unique in each case, and it is of a threshold form in the sense that for each value of the information, it is best to join either for all types of customers, only for those who are sufficiently price sensitive, only for those who are sufficiently delay sensitive, or for none. The optimal fee is also unique in nontrivial cases. This enables us to perform comparisons across different information structures. Managerial implications: The effect of heterogeneity depends highly on model parameters as well as the available information. For a fixed fee, an increase in heterogeneity has a positive overall impact on the customer population, whereas the effect on the revenue can be positive (slow service at a high fee) or negative (fast service at a low fee). Unlike with fixed fee, for the optimal fee, an increase in heterogeneity can have a negative overall effect on customers. Ignoring heterogeneity can lead to a substantial opportunity loss for the system.