Fair and efficient sharing: Dynamic pricing control for batch service system with strategic customers

Abstract

Motivated by the application of shared-type transportation, such as shuttle bus or ride-sharing, we propose a dynamic pricing control model by applying a strategic joining/balking scheme in which the fees for each customer and time of service commencement depend on their experienced waiting time cost in batch service (shuttle) systems. In this model, the monopolist sets the fee for each customer so that all customers on the same shuttle have equal experienced utility (including waiting costs), i.e., perfect experienced fairness among customers in the same batch is guaranteed. If the total waiting time cost for waiting customers exceeds a certain threshold, the monopolist allows the shuttle to depart, even if the number of customers is less than the full capacity (i.e., early departure), which can not only reduce the waiting cost but also achieve the experienced fairness among customers while guaranteeing the revenue and experienced utility. This study aims to verify the superiority of the dynamic pricing control model. We present a unique Nash equilibrium strategy, an algorithm for the transition probability, and effective approximations for the expected inter-arrival times of customers, conditional on the occurrence of early departure under the restriction that early departure can be executed only immediately before the arrival of the next customer. Then, we derive several performance measures to evaluate the dynamic pricing control model. Through numerical experiments, we confirm that our analytical results closely align with those of the general model, in which the timing of early departure is not restricted—implying the usefulness of our theoretical analysis. Moreover, we demonstrate that the dynamic pricing control model is superior to the conventional fixed pricing control model in terms of experienced fairness to customers and performance efficiency (for society, monopolist, and customers).