Dynamic Pricing under a Static Calendar
58 Pages Posted: 26 Oct 2018 Last revised: 18 Jul 2019
Date Written: October 2, 2018
This work is motivated by our collaboration with a large Consumer Packaged Goods (CPG) company. We have found that while they appreciate the advantages of dynamic pricing, they deem it operationally much easier to plan out a static price calendar 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 optimum under non-stationary demand, with both guarantees approaching 1 if the starting inventory is large.
A main contribution of this work is developing a system of tools for establishing best-possible performance guarantees relative to linear programming relaxations: in the stationary setting, structural properties about static policies which provide a complete characterization of tight bounds; and in the non-stationary setting, an adaptation of the prophet inequalities from optimal stopping theory to pricing and assortment problems.
Finally, we demonstrate on data from the CPG company that our simple price calendars are effective.
Keywords: revenue management, dynamic pricing, dynamic assortment, adaptivity
Suggested Citation: Suggested Citation