  The last-mile problem refers to the provision of travel service from the
nearest public transportation node to home or other destination. Last-Mile
Transportation Systems (LMTS), which have recently emerged, provide on-demand
shared transportation. In this paper, we investigate the fleet sizing and
allocation problem for the on-demand LMTS. Specifically, we consider the
perspective of a last-mile service provider who wants to determine the number
of servicing vehicles to allocate to multiple last-mile service regions in a
particular city. In each service region, passengers demanding last-mile
services arrive in batches, and allocated vehicles deliver passengers to their
final destinations. The passenger demand (i.e., the size of each batch of
passengers) is random and hard to predict in advance, especially with limited
data during the planning process. The quality of fleet allocation decisions is
a function of vehicle fixed cost plus a weighted sum of passenger's waiting
time before boarding a vehicle and in-vehicle riding time. We propose and
analyze two models-a stochastic programming model and a distributionally robust
optimization model-to solve the problem, assuming a known and unknown
distribution of the demand, respectively. We conduct extensive numerical
experiments to evaluate the models and discuss insights and implications into
the optimal fleet sizing and allocation for the on-demand LMTS under demand
uncertainty.
