Dynamic Pricing (and Assortment) Under a Static Calendar

Abstract

This work is motivated by our collaboration with a large consumer packaged goods (CPG) company. We have found that whereas 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 demand, and 1/2 of the optimum under nonstationary 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 stationary demand 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. This paper was accepted by Hamid Nazerzadeh, big data analytics.

Two-stage Matching and Pricing with Applications to Ride Hailing

“…This analysis is later improved and generalized by Ma and Simchi-Levi (2020) Prophet inequality. The results in two-stage joint matching/pricing (Section 5) resembles some aspects of ex-ante prophet inequalities for single item and matroid environment (Dütting et al 2017, Lee and Singla 2018, Chawla et al 2010, Kleinberg and Weinberg 2019, Correa et al 2017, prophet inequality matching (Alaei et al 2012), the Magician's problem (Alaei 2014), the pricing with static calendar problem (Ma et al 2021) (which also studies static assortment policies without reusable resources), and the volunteer crowdsourcing problem (Manshadi and Rodilitz 2020). Similar ex ante relaxation programs have been used for various stochastic online optimization and mechanism design problems.…”

“…The algorithm in Step (ii) is a special case for k = 1. The overall approach (i.e., lossless randomized rounding with an inner discarding procedure to guarantee the feasibility) has also been used in other stochastic online optimization problems and combinatorial variants of prophet inequality (e.g., Alaei et al 2012, Dütting et al 2017, Ma et al 2021, Feng et al 2019. The closest to us in this literature are Alaei et al (2012) and more recently, Ezra et al (2020) 7 , which use this technique for the prophet inequality matching problem under vertex arrival and edge arrival.…”

“…For example, see Alaei et al (2012), Feldman et al (2016), Dütting et al (2017), Lee and Singla (2018), Vera and Banerjee (2021), Ma et al (2021), Anari et al (2019). See Correa et al (2019) for a survey on recent developments in the literature on prophet inequalities.…”

Group-level Fairness Maximization in Online Bipartite Matching

“…Proof of Lemma 4. Part (1) follows from the simple fact (see e.g., [Ma et al, 2020]) that The last inequality is due to [Canonne, 2020]. Thus, by replacing λ with b/s, we establish Part (6).…”

Equity Promotion in Online Resource Allocation

“…Proof. (P1) is due to the work (Ma, Simchi-Levi, and Zhao 2021) (See the proof of Theorem 1 there). Next, we show (P2).…”