Efficient Formulations for Constrained Pricing under Attraction Demand Models

We propose a modeling and optimization framework to cast a broad range of fundamental multiproduct pricing problems as tractable convex optimization problems. We consider the basic setting of a retailer offering an assortment of differentiated substitutable products to a population of customers that are price-sensitive. The retailer selects prices to maximize profits, subject to constraints on sales arising from inventory and capacity availability, market share goals, bounds on allowable prices and other considerations. The goal is to use pricing to shape demand in order to better match constraints and maximize profits over a single period. This work shows, both theoretically and empirically, the tractability of large-scale constrained price optimization under the commonly used family of attraction demand models. The class of models includes the ubiquitous multinomial logit demand model. The treatment of arbitrary linear constraints on sales represents an important generalization of existing methods which usually focus only on limited classes of constraints such as individual product inventories, or at most joint capacity constraints. Our framework lends itself to adaptation in common heuristic approaches for multi-period stochastic pricing problems based on re-solving the certainty-equivalent problem, while significantly increasing modeling power at reasonable computational cost. ∗Operations Research Center, Massachusetts Institute of Technology †Sloan School of Management, Massachusetts Institute of Technology