Spring 2013 Seminar Series

DATE: April 18th
LOCATION: E51-315
TIME: 4:15pm
Reception immediately following

SPEAKER:
Guillermo Gallego

TITLE
Assortment and Pricing Optimization for the Nested Logit Model

ABSTRACT
We study assortment and pricing problems under variants of the nested logit (NL) choice model. The objective of the assortment problem is to find a set of product offerings that maximizes the expected revenue per customer assuming fixed prices. The pricing problem allows prices to be decision variables. We show that the assortment problem is polynomially solvable for the standard NL model (dissimilarity parameters less than one and customers purchasing from the selected nest). Relaxing either assumption renders the problem NP-hard. For the hard cases, we develop parsimonious collections of candidate assortments with worst-case performance guarantees. We then study assortment problems with cardinality, precedence and space constraints for the standard NL model. We show that an optimal assortment under cardinality or precedence constraints can be obtained by solving a linear program. We show that the problem is NP-hard under space constraints and provide a 2-approximation algorithm for this case. For the pricing problem we show that the adjusted markup (defined as the price minus variable cost minus the reciprocal of the price sensitivity) is constant for all products within a nest. We also show that each nest has an adjusted nest-level markup that is nest invariant. These results reduce a non-linear, non-concave, multi-variable optimization problem to the optimization of a single dimensional continuous function over a bounded interval. We provide conditions under which this function is unimodal. For competitive settings, we use our results to simplify the oligopolistic price competition problem, characterize the Nash Equilibrium (NE), and provide conditions under which the tatonnement process converges to the NE. (Joint work with J. Davis and H. Topaloglu; Ruxian Wang)