The Exponomial Choice Model: A New Alternative for Assortment and Price Optimization

Abstract

We investigate the use of a canonical version of a discrete choice model due to Daganzo (1979) [Daganzo C (1979) Multinomial Probit: The Theory and Its Application to Demand Forecasting (Academic Press, New York).] in optimal pricing and assortment planning. In contrast to multinomial and nested logit (the prevailing choice models used for optimizing prices and assortments), this model assumes a negatively skewed distribution of consumer utilities, an assumption we motivate by conceptual arguments as well as published work. The choice probabilities in this model can be derived in closed form as an exponomial (a linear function of exponential terms). The pricing and assortment planning insights we obtain from the exponomial choice (EC) model differ from the literature in two important ways. First, the EC model allows variable markups in optimal prices that increase with expected utilities. Second, when prices are exogenous, the optimal assortment may exhibit leapfrogging in prices, i.e., a product can be skipped in favor of a lower-priced one depending on the utility positions of neighboring products. These two plausible pricing and assortment patterns are ruled out by multinomial logit (and by nested logit within each nest). We provide structural results on optimal pricing for monopoly and oligopoly cases, and on the optimal assortments for both exogenous and endogenous prices. We also demonstrate how the EC model can be easily estimated—by establishing that the log-likelihood function is concave in model parameters and detailing an estimation example using real data.

Assortment optimization under the Sequential Multinomial Logit Model

“…The assortment optimization problem under the Manzini and Mariotti model has been recently studied by Gallego and Li (2017), where they show that revenue-ordered assortments strategy is optimal. Another choice model studied is the negative exponential distribution (NED) model (Daganzo, 1979), also known as the Exponomial model (Alptekinoglu and Semple, 2016) in which customer utilities follow negatively skewed distribution. Alptekinoglu and Semple (2016) proved that when prices are exogenous, the optimal assortment might not be revenue-ordered assortment, because a product can be skipped in favour of a lower-priced one depending on the utilities.…”

“…Another choice model studied is the negative exponential distribution (NED) model (Daganzo, 1979), also known as the Exponomial model (Alptekinoglu and Semple, 2016) in which customer utilities follow negatively skewed distribution. Alptekinoglu and Semple (2016) proved that when prices are exogenous, the optimal assortment might not be revenue-ordered assortment, because a product can be skipped in favour of a lower-priced one depending on the utilities. This last result differs from what happens under the MNL and the Nested Logit Model (within each nest).…”

A strong Lagrangian relaxation for general discrete-choice network revenue management

“…Each segment has a preference weight (ideal utility) associated with purchasing a product that is in its consideration set and a preference weight associated with not purchasing anything. However, each segment's choice is governed by the exponomial choice model (Alptekinoğlu and Semple [2]). That is, if the preference weights are ordered so that…”

“…where n g is the number of products in the consideration set of segment g that are part of the offer set, then the probability that a segment g arrival purchases product j when S is the offer set is (Alptekinoğlu and Semple [2])…”

Consumer Choice Under Limited Attention When Options Have Different Information Costs

“…MNL and its variations (e.g., nested logit) have been extensively used to model consumer behavior in the operations management literature as well, in particular in the context of pricing, revenue management and assortment planning (Hanson and Martin 1996, van Ryzin and Mahajan 1999, Dong et al 2009, Zhang and Adelman 2009, Davis et al 2014. In this stream, the need for richer and more general choice models has also been recognized and some propositions have been made, such as Talluri and van Ryzin (2004), Alptekinoğlu and Semple (2015), Blanchet et al (2016), Srikanth and Rusmevichientong (2016). Our paper complements this literature by offering a new, general and versatile choice model that is derived from an analysis of the optimal behaviour of an individual consumer.…”