Product-Line Pricing Under Discrete Mixed Multinomial Logit Demand

Abstract

We study a product-line price optimization problem with demand given by a discrete mixed multinomial logit (MMNL) model. The market is divided into a finite number of market segments, with product demand in each segment governed by the multinomial logit (MNL) model. We show that the concavity property with respect to the choice probability vector shown for the MNL model breaks down under MMNL even for entirely symmetric price sensitivities. In addition, the equal markup property identified for the MNL model no longer holds under MMNL, suggesting that heterogeneity in customer population justifies non-equal-markup pricing. In this paper, we characterize the profit function under MMNL as the sum of a set of quasiconcave functions and present efficient optimization algorithms. We demonstrate the application of our methods using data from Intel Corporation. Our results show that the optimal prices exploit segment differences through redistribution of sales and profit among customer segments. In addition, we use our methods to generate the profit-share efficient frontier, helping the firm to set prices that effectively balance these two measures. The tools developed in this research function in three important ways at Intel: (1) they provide a new alternative for market share prediction among Intel products for different customer segments, adding to the suite of independent demand forecasting tools; (2) they optimize product prices based on segment-specific customer preferences revealed through sales data, a capability that Intel’s current pricing tools include only heuristically; (3) they quantify the trade-off between profit and market share, adding a new decision support capability to the company. The online appendix is available at https://doi.org/10.1287/msom.2017.0675 .