Dynamic Pricing under a Static Calendar

Our work is based on the classical dynamic pricing problem. From our collaborations with a large Consumer Packaged Goods company, we have found that while they appreciate the advantages of dynamic pricing, it is operationally beneficial for them to plan out a deterministic price calendar in advance. Motivated by this, we formulate the dynamic pricing problem under static calendar constraints, where instead of doing closed-loop control, we are now doing open-loop control. We study how classical dynamic pricing intuitions may hold, or fail. We distinguish two cases: stationary and non-stationary arrivals. Then we propose two constant-factor approximation heuristics, and their corresponding asymptotic optimality analyses, under both cases. The bounds we obtain are tight, and they match the bounds of classical dynamic pricing model. Finally, we generalize our model in two different ways. First, the customer purchase can be not only Bernoulli random variables, but also arbitrary random variables with bounded support. Second, instead of offering different prices, we can offer an assortment of products, and customer chooses one of them. Under both generalizations, our heuristics still work, by giving us the exact same bounds.