Technical Note—A Note on Relaxations of the Choice Network Revenue Management Dynamic Program

Kunnumkal, S and Talluri, K (2016) Technical Note—A Note on Relaxations of the Choice Network Revenue Management Dynamic Program. Operations Research, 64 (1). pp. 158-166. ISSN 1526-5463

Full text not available from this repository. (Request a copy)


In recent years, several approximation methods have been proposed for the choice network revenue management problem. These approximation methods are proposed because the dynamic programming formulation of the choice network revenue management problem is intractable even for moderately sized instances. In this paper, we consider three approximation methods that obtain upper bounds on the value function, namely, the choice deterministic linear program (CDLP), the affine approximation (AF), and the piecewise-linear approximation (PL). It is known that the piecewise-linear approximation bound is tighter than the affine bound, which in turn is tighter than CDLP. In this paper, we prove bounds on how much the affine and piecewise-linear approximations can tighten CDLP. We show (i) the gap between the AF and CDLP bounds is at most a factor of 1+1/(miniri1), where ri1>0 are the resource capacities, and (ii) the gap between the piecewise-linear and CDLP bounds is within a factor of 2. Moreover, we show that these gaps are essentially tight. Our results hold for any discrete-choice model and do not involve any asymptotic scaling. Our results are surprising because calculating the AF bound is NP-hard and CDLP is tractable for a single-segment multinomial logit model; our result implies that if a firm has all resource capacities of 100, the gap between the two bounds, however, is at most 1.01.

Item Type: Article
Subjects: Operations Management > Product Development
Operations Management > Supply Chain Management
Date Deposited: 02 Apr 2019 15:00
Last Modified: 11 Jul 2023 17:49

Actions (login required)

View Item
View Item