A Note on State-Independent Policies in Network Revenue Management
Forthcoming in Operations Research
28 Pages Posted: 22 Apr 2021 Last revised: 23 Mar 2023
Date Written: April 21, 2021
Abstract
We revisit the price-based and choice-based network revenue management problems studied in Gallego and Van Ryzin (1997) [GvR] and Liu and Van Ryzin (2008) [LvR], respectively. The setting is as follows: A firm sells multiple products over a finite horizon using a limited supply of resources. Product demands are stochastic. The demand rate for each product depends on the current price-vector (resp., assortment displayed). The firm's goal is to obtain a pricing (resp., assortment) policy that maximizes its expected revenue. GvR's main result is that the optimality gaps incurred by two state-independent policies scale proportionally to $\sqrt{k}$, where $k$ is the scale of demand and supply. GvR's analysis implicitly assumes that the demand-price relationship is separable among the products. In this paper, we derive GvR's results for the more general setting where the demand-price relationship need not be separable. We also consider an important practical variant of GvR's problem in which the price of each product is restricted to a discrete and finite set, and show the $\sqrt{k}$ result for this problem. For the assortment problem studied in LvR, to our knowledge, there is no result in the literature on the asymptotic convergence rate of any policy. We show that LvR's problem is mathematically equivalent to the discrete-price variant of GvR's problem and use this equivalence to show that LvR's CDLP policy also inherits the $\sqrt{k}$ bound on the optimality gap.
Keywords: multi-product dynamic pricing, network revenue management, static policies
JEL Classification: C61
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