  Same-day delivery for e-commerce has become a popular service. Companies
usually offer several time delivery options with the earliest one being next
hour delivery. Due to tight delivery deadlines and thin margins, companies
often find it challenging to provide efficient same-day delivery services. In
this work, we propose a holistic scheme that combines the optimization of
routing and pricing for same-day delivery. The proposed approach is able to
take into account uncertainty in travel times, a crucial factor for delivery
applications in urban environments. We model this problem as a Markov decision
process. We apply a value function approximation technique to compute
opportunity costs. Based on these opportunity costs, as well as the customer
choice model and travel time distribution, we optimize the prices for various
delivery deadlines. We perform extensive computational experiments to compare
the proposed model with baseline policies. We also investigate how the
(potentially wrong) choice of travel time distributions affect the performance
of the proposed optimization scheme. Through numerical simulations of realistic
scenarios, we observe that compared to the deterministic model, the proposed
approach can reduce the number of missed deliveries up to 40%; at the same
time, it can increase revenue by more than 5% compared to the baseline
policies. We explore new issues that arise due to the stochastic nature of the
problem such as the effect of penalties for missed deliveries on pricing
structure and overall revenue.
