  This work is motivated by our collaboration with a large consumer packaged
goods (CPG) company. We have found that while the company appreciates the
advantages of dynamic pricing, they deem it operationally much easier to plan
out a static price calendar in advance.
  We investigate the efficacy of static control policies for revenue management
problems whose optimal solution is inherently dynamic. In these problems, a
firm has limited inventory to sell over a finite time horizon, over which
heterogeneous customers stochastically arrive. We consider both pricing and
assortment controls, and derive simple static policies in the form of a price
calendar or a planned sequence of assortments, respectively. In the assortment
planning problem, we also differentiate between the static vs. dynamic
substitution models of customer demand. We show that our policies are within
1-1/e (approximately 0.63) of the optimum under stationary (IID) demand, and
1/2 of the optimum under non-stationary demand, with both guarantees
approaching 1 if the starting inventories are large.
  We adapt the technique of prophet inequalities from optimal stopping theory
to pricing and assortment problems, and our results are relative to the linear
programming relaxation. Under the special case of IID single-item pricing, our
results improve the understanding of irregular and discrete demand curves, by
showing that a static calendar can be (1-1/e)-approximate if the prices are
sorted high-to-low.
  Finally, we demonstrate on both data from the CPG company and synthetic data
from the literature that our simple price and assortment calendars are
effective.
