On submodular function minimization
Combinatorica
Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Revenue Management: Research Overview and Prospects
Transportation Science
Single-minded unlimited supply pricing on sparse instances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Buying cheap is expensive: hardness of non-parametric multi-product pricing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal envy-free pricing with metric substitutability
Proceedings of the 9th ACM conference on Electronic commerce
On the approximability of the maximum feasible subsystem problem with 0/1-coefficients
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
An Optimal Approximate Dynamic Programming Algorithm for the Lagged Asset Acquisition Problem
Mathematics of Operations Research
On Profit-Maximizing Pricing for the Highway and Tollbooth Problems
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Robust Controls for Network Revenue Management
Manufacturing & Service Operations Management
A quasi-PTAS for profit-maximizing pricing on line graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Maximum utility product pricing models and algorithms based on reservation price
Computational Optimization and Applications
Proceedings of the forty-third annual ACM symposium on Theory of computing
Optimal Envy-Free Pricing with Metric Substitutability
SIAM Journal on Computing
How to sell a graph: guidelines for graph retailers
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Buying Cheap Is Expensive: Approximability of Combinatorial Pricing Problems
SIAM Journal on Computing
A QPTAS for ε-envy-free profit-maximizing pricing on line graphs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
On the complexity of the highway problem
Theoretical Computer Science
Blind Network Revenue Management
Operations Research
A Nonparametric Approach to Modeling Choice with Limited Data
Management Science
Blind Network Revenue Management
Operations Research
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Developed by General Motors (GM), the Auto Choice Advisor website (http://www.autochoiceadvisor.com) recommends vehicles to consumers based on their requirements and budget constraints. Through the website, GM has access to large quantities of data that reflect consumer preferences. Motivated by the availability of such data, we formulate a nonparametric approach to multiproduct pricing. We consider a class of models of consumer purchasing behavior, each of which relates observed data on a consumers requirements and budget constraint to subsequent purchasing tendencies. To price products, we aim at optimizing prices with respect to a sample of consumer data. We offer a bound on the sample size required for the resulting prices to be near-optimal with respect to the true distribution of consumers. The bound exhibits a dependence of O(n log n) on the number n of products being priced, showing thatin terms of sample complexitythe approach is scalable to large numbers of products. With regards to computational complexity, we establish that computing optimal prices with respect to a sample of consumer data is NP-complete in the strong sense. However, when prices are constrained by a price ladderan ordering of prices defined prior to price determinationthe problem becomes one of maximizing a supermodular function with real-valued variables. It is not yet known whether this problem is NP-hard. We provide a heuristic for our price-ladder-constrained problem, together with encouraging computational results. Finally, we apply our approach to a data set from the Auto Choice Advisor website. Our analysis provides insights into the current pricing policy at GM and suggests enhancements that may lead to a more effective pricing strategy.