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A new compact linear programming formulation for choice network revenue management

Sumit Kunnumkal and Kalyan Talluri ()

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

Abstract: The choice network revenue management model incorporates customer purchase behavior as a function of the offered products, and is the appropriate model for airline and hotel network revenue management, dynamic sales of bundles, and dynamic assortment optimization. The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalence relaxation of the dynamic program, called the choice deterministic linear program (CDLP) is usually used to generate dyamic controls. Recently, a compact linear programming formulation of this linear program was given for the multi-segment multinomial-logit (MNL) model of customer choice with non-overlapping consideration sets. Our objective is to obtain a tighter bound than this formulation while retaining the appealing properties of a compact linear programming representation. To this end, it is natural to consider the affine relaxation of the dynamic program. We first show that the affine relaxation is NP-complete even for a single-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a new compact linear program that approximates the dynamic programming value function better than CDLP, provably between the CDLP value and the affine relaxation, and often coming close to the latter in our numerical experiments. When the segment consideration sets overlap, we show that some strong equalities called product cuts developed for the CDLP remain valid for our new formulation. Finally we perform extensive numerical comparisons on the various bounds to evaluate their performance.

JEL-codes: C61 L83 L93 M11 (search for similar items in EconPapers)
Date: 2012-12
New Economics Papers: this item is included in nep-cmp, nep-tre and nep-tur
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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