Joint Pricing and Routing for a Ride-Sharing Platform in Low-Density Rural Areas

In low-density rural areas, implementing traditional public transportation can be challenging due to the first-and-last-mile problem. With the development of transformative technologies, an online ride-sharing platform can be a solution to address the rural mobility problem by offering on-demand and shared services. Accordingly, in this paper, we integrate dynamic pricing and assortment with a dynamic routing problem allowing for deadline decisions in a unified framework for an online ride-sharing problem. This framework considers a ride-sharing platform that dynamically offers multiple vehicle options with different prices, promised pick-up times, and promised drop-off times to a request in a rural area. The request then selects one of those options or leaves the platform with no selection. The ride-sharing platform's decisions in the current period will impact both the present and future requests' decisions. To this end, we design a policy that can influence requests' choice behavior and efficiently assign the vehicles. We model the problem as a Markov decision process (MDP) and assume that the request's choice is made based on the multinomial logit (MNL) model. By exploiting the MNL structure, we develop an anticipatory dynamic pricing and routing (ADPR) policy consisting of an efficient routing heuristic, a buffer time policy to determine promised pick-up and drop-off times, and the corresponding optimal pricing and assortment policy. Since state-dependent opportunity costs are required to apply the ADPR policy, we use a value function approximation method based on state-space aggregation to estimate the value of each state. The ADPR policy is able to make all decisions in real time when a request enters the platform. We compare the ADPR policy with four benchmark policies in a comprehensive numerical study, and the ADPR policy outperforms the benchmark policies significantly