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Bounds and Heuristics for Multi-Product Personalized Pricing

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Document pages: 16 pages

Abstract: We present tight bounds and heuristics for personalized, multi-productpricing problems. Under mild conditions we show that the best price in thedirection of a positive vector results in profits that are guaranteed to be atleast as large as a fraction of the profits from optimal personalized pricing.For unconstrained problems, the fraction depends on the factor and on optimalprice vectors for the different customer types. For constrained problems thefactor depends on the factor and a ratio of the constraints. Using a factorvector with equal components results in uniform pricing and has exceedinglymild sufficient conditions for the bound to hold. A robust factor is presentedthat achieves the best possible performance guarantee. As an application, ourmodel yields a tight lower-bound on the performance of linear pricing relativeto optimal personalized non-linear pricing, and suggests effective non-linearprice heuristics relative to personalized solutions. Additionally, our modelprovides guarantees for simple strategies such as bundle-size pricing andcomponent-pricing with respect to optimal personalized mixed bundle pricing.Heuristics to cluster customer types are also developed with the goal ofimproving performance by allowing each cluster to price along its own factor.Numerical results are presented for a variety of demand models that illustratethe tradeoffs between using the economic factor and the robust factor for eachcluster, as well as the tradeoffs between using a clustering heuristic with aworst case performance of two and a machine learning clustering algorithm. Inour experiments economically motivated factors coupled with machine learningclustering heuristics performed best.

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