Technical Note—A Note on State-Independent Policies in Network Revenue Management

We revisit two classical price-based and choice-based network revenue management problems studied in the literature. The setting for the problems 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 (respectively, assortment displayed). The firm's goal is to obtain a pricing (respectively, assortment) policy that maximizes its expected revenue. The main result for the price-based problem 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. The analysis in the literature implicitly assumes that the demand-price relationship is separable among the products. In this paper, we derive these results for the more general setting where the demand-price relationship need not be separable. We also consider an important practical variant of the price-based 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 choice-based problem, to our knowledge, there is no result in the literature on the asymptotic convergence rate of any policy. We show that this problem is mathematically equivalent to the discrete-price variant of the price-based problem and use this equivalence to show that the choice-based deterministic linear program policy in the literature for the choice-based problem also inherits the $\sqrt{k}$ bound on the optimality gap.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2471.