Data-Driven Dynamic Pricing and Ordering with Perishable Inventory in a Changing Environment

We consider a retailer that sells a perishable product, making joint pricing and inventory ordering decisions over a finite time horizon of T periods with lost sales. Exploring a real-life data set from a leading supermarket chain, we identify several distinctive challenges faced by such a retailer that have not been jointly studied in the literature: the retailer does not have perfect information on (1) the demand-price relationship, (2) the demand noise distribution, (3) the inventory perishability rate, and (4) how the demand-price relationship changes over time. Furthermore, the demand noise distribution is nonparametric for some products but parametric for others. To tackle these challenges, we design two types of data-driven pricing and ordering (DDPO) policies for the cases of nonparametric and parametric noise distributions. Measuring performance by regret, that is, the profit loss caused by not knowing (1)-(4), we prove that the T-period regret of our DDPO policies are in the order of T-2/3 (log T)(1/2) and T(1/2)log T in the cases of nonparametric and parametric noise distributions, respectively. These are the best achievable growth rates of regret in these settings (up to logarithmic terms). Implementing our policies in the context of the aforementioned real-life data set, we show that our approach significantly outperforms the historical decisions made by the supermarket chain. Moreover, we characterize parameter regimes that quantify the relative significance of the changing environment and product perishability. Finally, we extend our model to allow for age-dependent perishability and demand censoring and modify our policies to address these issues.

Automated summary

This study examines the challenges faced by retailers selling perishable products, including uncertainty in demand-price relationship, demand noise distribution, inventory perishability rate, and changes in demand-price relationship over time. To address these challenges, two data-driven pricing and ordering policies are designed, and their performance is evaluated using regret. The empirical results show that the proposed policies outperform historical decisions, and parameter regimes for quantifying the relative significance of changing environment and product perishability are characterized.