Spatio-temporal pricing algorithm for ride-hailing platforms where drivers can decline ride requests

This study develops an algorithm to determine the pricing policy and matching rate for ride-hailing platforms to maximize their profitability by considering: (a) drivers’ decisions to accept or decline requests, (b) the spatio-temporal characteristics of networks, and (c) dynamic fleet size. We take into account the impact of pricing policy on demand, matching rate, drivers’ income, fleet size, and the distribution of drivers as the result of relocations and accepted rides, in a time-varying interconnected network. First, we transform the problem into an equivalent time-invariant one. Then, we illustrate the relationship between the optimal fares and the optimal compensation and develop an iterative algorithm to efficiently determine a near-optimal amount for fare, compensation, and matching rate for each ride. Moreover, we introduce a balanced demand pattern to highlight concordant inbound and outbound ride flows in network locations and show that the maximum profit is obtained with a balanced demand in the network. We prove that in a balanced network, drivers earn their expected income with less traveled distance if they have the option to decline rides, which implies a higher expected profit for drivers. The performance of our proposed algorithm is evaluated by applying it to the data of a real-world ride-hailing platform. We also show that the recommended pricing policy leads to profit as high as 99% of a similar case with balanced demand (as an upper limit), when applied to a real network with a light demand imbalance.