  We build a parsimonious model of a stochastic e-commerce fulfillment center
offering time-dependent shipment options and corresponding fees to
utility-maximizing customers that arrive according to a Poisson process. For
this time-dependent policy, we present an exact analysis based on the
underlying periodic Markov chain as well as monotonicity results for the
optimal time-dependent shipment fee structure. We then propose a simple
time-dependent shipment policy with an attractive two-level fee structure, and
study it alongside two benchmarks that are prevalent in practice. Both
benchmarks rely on static, time-independent fees for the offered shipment
options, but differ in whether they stop offering same-day shipment after a
certain cutoff time. Our numerical analysis indicates that including such a
cutoff point under static shipment fees increases profits significantly, and
that moving to time-dependent shipment fees increases profits by another
substantial amount. Our time-dependent policy provides e-commerce companies
with an easily implementable mechanism to better manage online demands for
same-day or next-day shipment with the available capacity in the fulfillment
centers responsible for collecting and shipping those orders.
