NDLI: Efficient formulations for pricing under attraction demand models

Content Provider	Springer Nature Link
Author	Perakis, Georgia Levi, Retsef Keller, Philipp W.
Copyright Year	2013
Abstract	We propose a modeling and optimization framework to cast a broad range of fundamental multi-product pricing problems as tractable convex optimization problems. We consider 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. Consumers’ response to price changes is represented by attraction demand models, which subsume the well known multinomial logit (MNL) and multiplicative competitive interaction demand models. Our approach transforms seemingly non-convex pricing problems (both in the objective function and constraints) into convex optimization problems that can be solved efficiently with commercial software. We establish a condition which ensures that the resulting problem is convex, prove that it can be solved in polynomial time under MNL demand, and show computationally that our new formulations reduce the solution time from days to seconds. We also propose an approximation of demand models with multiple overlapping customer segments, and show that it falls within the class of demand models we are able to solve. Such mixed demand models are highly desirable in practice, but yield a pricing problem which appears computationally challenging to solve exactly.
Ending Page	261
Page Count	39
Starting Page	223
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	145
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-03-29
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computational methods Theoretical, Mathematical and Computational Physics Multinomial logit Consumer behavior, demand theory Mathematical Methods in Physics Calculus of Variations and Optimal Control; Optimization Mathematics of Computing Numerical Analysis Pricing Revenue management Nonlinear programming Attraction demand models Combinatorics Price theory and market structure
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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