Assortment and Pricing Optimization
Guillermo Gallego, Columbia University, United States
Date:
18 Nov 2013
Time:
4.00pm – 5.00pm
Venue:
S17-04-06
(This seminar is organized jointly with the Department of Decision Sciences)
About the Speaker
Professor Guillermo Gallego joined Columbia University IEOR Department in 1988, where he has been conducting research in the areas of inventory theory, supply chain management, revenue management, and dynamic pricing. He was named an Informs Fellow in 2012 and and MSOM Fellow in 2013. He has been the recipient of many awards including the Informs Revenue Management Section Prize (2005), the Revenue Management Historical Prize (2011) and the Revenue Management Practice Prize (2012). Professor Gallego has published influential papers in the leading journals of his field where he has also occupied a variety of editorial positions. His work has been supported by numerous industrial and government grants. Professor Gallego has consulted for Hewlett Packard, IBM, Lucent, Nomis Solutions, and Sabre Airline Solutions. He has also worked with government agencies such as the National Research Council, the National Science Foundation and the Ireland Development Agency. His graduate students are associated with prestigious universities. He spent his 1996–97 sabbatical at Stanford University and was a visiting scientist at the IBM Watson Research Center from 1999 to 2003. He was the chairman of the IEOR Department from July 2002 to June 2008.
Abstract
We study assortment and pricing problems under variants of the multinomial logit (MNL) and nested logit (NL) choice models. The objective of the assortment problem is to find a set of product offerings that maximize the expected revenue per customer assuming fix prices. The pricing problem allows prices to be decision variables. For the MNL model we consider formulations that have totally unimodular constraints. Applications include joint location and assortment problems and joint pricing and assortment problems. We show that the binary fractional program can be reformulated as linear program. For the standard NL model we show that the unconstrained problem is polynomially solvable. We show that optimal assortments under cardinality or precedence constraints can be solved via linear programming, and that the problem is NP-hard under space constraints. We also show that non-standard versions (dissimilarity parameters greater than one or no-purchase alternative within the selected nest) are NP-hard. For the hard cases, we develop parsimonious collections of candidate assortments with worst-case performance guarantees. For the pure pricing problem for the NL model we show that the adjusted markup (defined as the price minus cost minus the reciprocal of the price sensitivity) is constant for all products within a nest. We also show that adjusted nest-level markups are nest invariant. These results reduce a non-linear, non-convave, multi-variable optimization problem to the optimization of a single dimensional continuous function over a bounded interval. We provide conditions for this function to be unimodal. We use these results to simplify the oligopolistic price competition problem, characterize the NE, and provide conditions for the tatonnement process to coverage to the NE. Based on several papers written with: James Davis, Huseyin Topaloglu and Ruxian Wang
