Dynamic Pricing for Nonperishable Products with Demand Learning

Abstract

A retailer is endowed with a finite inventory of a nonperishable product. Demand for this product is driven by a pricesensitive Poisson process that depends on an unknown parameter that is a proxy for the market size. The retailer has a prior belief on the value of this parameter that he updates as time and available information (prices and sales) evolve. The retailer's objective is to maximize the discounted long-term average profits of his operation using dynamic pricing policies. We consider two cases. In the first case, the retailer is constrained to sell the entire initial stock of the nonperishable product before a different assortment is considered. In the second case, the retailer is able to stop selling the nonperishable product at any time and switch to a different menu of products. For both cases, we formulate the retailer's problem as a (Poisson) intensity control problem and derive structural properties of an optimal solution, and suggest a simple and efficient approximated solution. We use numerical computations, together with asymptotic analysis, to evaluate the performance of our proposed policy.

Dynamic pricing and learning: Historical origins, current research, and new directions

“…Araman and Caldentey (2009) consider a two-point prior distribution, whereas Farias and van Roy (2010) assume that the prior is a finite mixture of gamma distributions; in both settings, the posterior distributions are in the same parametric family as the prior, which makes the problem tractable. Araman and Caldentey (2009) propose a pricing heuristic based on an asymptotic approximation of the value function of the corresponding intensity control problem.…”

Dynamic Pricing and Learning: Historical Origins, Current Research, and New Directions

“…Farias and van Roy (2010) propose another heuristic, called decay balancing, and show several numerical experiments that suggest that it often performs better than both the heuristic proposed by Araman and Caldentey (2009) and CEP. In addition they prove a performance bound on decay balancing,…”

“…Lobel and Perakis (2011) attempt to bridge the gap between robust and data-driven approaches to dynamic pricing, by considering a setting where the uncertainty set is deduced from data samples. A robust extension of Caldentey (2009) andvan Roy (2010), where finite inventory is sold during an infinite time horizon, is studied by Li et al (2009). Another approach that does not rely on historical demand data is Xiong et al (2010) (see also Li, 2010, Li et al, 2013).…”

Clearance Pricing Optimization for a Fast-Fashion Retailer

“…Note that the definition in Equation (29) has two components which normalize sales data with respect to inter-week as well as intra-week variations. Although these components should be updated every season, we have observed that they have remained in fact quite constant over the years (see Carboni 2009), which shows the formula's robustness and validates its use.…”