A State Aggregation Approach for Stochastic Multiperiod Last-Mile Ride-Sharing Problems

The arrangement of last-mile services is playing an increasingly important role in making public transport more accessible. We study the use of ridesharing in satisfying last-mile demands with the assumption that demands are uncertain and come in batches. The most important contribution of our paper is a two-level Markov decision process framework that is capable of generating a vehicle-dispatching policy for the aforementioned service. We introduce state summarization, representative states, and sample-based cost estimation as major approximation techniques in making our approach scalable. We show that our approach converges and solution quality improves as sample size increases. We also apply our approach to a series of case studies derived from a real-world public transport data set in Singapore. By examining three distinctive demand profiles, we show that our approach performs best when the distribution is less uniform and the planning area is large. We also demonstrate that a parallel implementation can further improve the performance of our solution approach. The online appendix is available at https://doi.org/10.1287/trsc.2018.0840 .