Transportation Science | November 2019
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.
Sumit Kunnumkal is a Professor and Area Leader of Operations Management at the Indian School of Business (ISB). He holds a PhD in Operations Research from Cornell University. He received his MS in Transportation from the Massachusetts Institute of Technology and a B.Tech in Civil Engineering from the Indian Institute of Technology, Madras.
Professor Kunnumkal has previously taught at the Smith School of Business, Queen’s University, and has held visiting positions at the Singapore University of Technology and Design and Universitat Pompeu Fabra. His research interests lie in the areas of pricing and revenue management, retail operations, assortment planning, and approximate dynamic programming.
At ISB, he has taught in the PGP programme, the Fellow programme, and various Advanced Management and Executive Education programmes.
