Dynamic Pricing under a Static Calendar
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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 is endowed with limited inventories 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 inventories are large. A main contribution of this work is developing a system of tools for establishing best-possible performance guarantees relative to linear programming relaxations; specifically, structural properties about static policies which provide a complete characterization of tight bounds in the stationary setting, and an adaptation of the well-known prophet inequalities from optimal stopping theory to pricing and assortment problems in the non-stationary setting. We also demonstrate on data provided by the CPG company that our simple price calendars are effective.
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