Time-of-Day Pricing in Taxi Markets

Abstract

For a regular weekday in New York City, the number of taxi trips at 8 P.M. may be 10 times greater than that at 5 A.M., while passengers are charged under the same pricing scheme. Motivated by temporally non-stationary demand and supply in the taxi market, the time-of-day (TOD) pricing scheme for taxi industry is framed to vary trip cost dynamically over time, so that total market revenue is maximized. Temporal market dynamics is modeled as a semi-Markov process, which captures leftover of drivers, spillover of passengers, and restoration of drivers in service along the time horizon. The TOD pricing scheme is therefore formulated as discrete time stochastic dynamic programming with the goal to find the optimal sequence of price multipliers. The approximate dynamic programming (ADP) approach is introduced to solve the curse of dimensionality. Numerical experiments are conducted using New York City taxi trip data to illustrate the effectiveness of TOD price in real-world taxi market. The results suggest that TOD price may increase daily market revenue by over 10% using the ADP approach. Our experiments also show that TOD price may be even more effective if sudden surges in demand take place in the market.