This work is motivated by our collaboration with a large consumer packaged goods (CPG) company. We found that while the company appreciates the advantages of dynamic pricing, they deem it operationally much easier to plan out a static price calendar / sequence of assortments in advance.

In this paper, we investigate the efficacy of static control policies for dynamic revenue management problems. In these problems, a firm has limited inventory to sell over a finite time horizon where demand is known but stochastic. 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. 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 inventory is large.

We adapt the technique of prophet inequalities from optimal stopping theory to pricing and assortment problems, and our results are very general, holding relative to the linear program relaxation and holding even if fractional amounts of inventory can be consumed at a time. In the special case of single-item pricing, we develop structural results regarding the optimal two-price calendar for irregular or discrete demand curves.

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.