Efficient formulations for pricing under attraction demand models
Name
10107_2013_646_ReferencePDF.pdf
Size
686.24 KB
Format
Adobe PDF
Checksum (MD5)
d11a56c6fbdbaad33845baad59e3f79c
Author(s)
Keller, Philipp W.
Levi, Retsef
Perakis, Georgia
Date Issued
March 2013
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Keller, Philipp W., Retsef Levi, and Georgia Perakis. “Efficient Formulations for Pricing Under Attraction Demand Models.” Math. Program. 145, no. 1–2 (March 29, 2013): 223–261.
Version
Author's final manuscript
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.
MIT Department
Sloan School of Management
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10107-013-0646-z
