Time-based or fixed-fee? How to penalize cancellation of orders of car-hailing applications

While waiting for an ordered ride service through a car hailing application (CHA), a customer may encounter a taxi. Hence, the customer may cancel the CHA order and take the taxi instead. CHAs often charge penalty fees for such order cancellations. In this paper, we study the effect of different cancellation penalty schemes on the system performance. Comparing different payment schemes is a classic OM topic but the past studies mainly focus on the one-sided market. Our question is new here as it studies the penalty schemes in a two-sided market, in which the demand-side customers’ cancellation behavior imposes costs on the supply-side drivers. Furthermore, a penalty scheme affects customers’ strategic behavior, which is modeled as a two-stage decision problem. We mainly adopt stochastic model to capture the stochastic system's performance and conduct optimization on customers’ and CHA platforms’ decisions. We first show that the penalty fee shall be equal to the CHA car driver's cost due to order cancellation so as to achieve the social cost minimization (or social welfare maximization). We then consider a special case with a linear time-dependent cost function for drivers, and study the optimal time-based scheme and the optimal fixed-fee scheme. We find that the fixed-fee scheme is likely to generate more users when the number of CHA cars is limited. In contrast, the time-based scheme encourages early cancellation and prevents late cancellation, performing the best in the social cost minimization.