A New Compact Linear Programming Formulation for Choice Network Revenue Management
AbstractThe 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 dynamic 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.
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Bibliographic InfoPaper provided by Barcelona Graduate School of Economics in its series Working Papers with number 677.
Date of creation: Dec 2012
Date of revision:
dynamic programming; network revenue management; approximation algorithms; discrete choice models;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- L93 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Air Transportation
- L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Recreation; Tourism
- M11 - Business Administration and Business Economics; Marketing; Accounting - - Business Administration - - - Production Management
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