NDLI: Assortment Optimisation under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

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Assortment Optimisation under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

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Assortment Optimisation under a General Discrete Choice Model: A Tight Analysis of Revenue-Ordered Assortments

Content Provider	ACM Digital Library
Author	Joret, Gwenaël Berbeglia, Gerardo
Abstract	The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue π and then choosing all products with revenue at least π. This is known as the revenue-ordered assortments strategy. Our first contribution is an analysis of the performance of the revenue-ordered assortments strategy making only minimal assumptions about the underlying discrete choice model: We assume that consumers behave rationally, in the sense that the probability of choosing a specific product x ∈ S when given a choice set S cannot increase if S is enlarged. This rationality assumption, known as regularity, is satisfied by almost all models studied in the revenue management and choice theory literature. This includes in particular all random utility models, as well as other models introduced recently such as the additive perturbed utility model, the hitting fuzzy attention model, and models obtained using a non-additive random utility function. We provide three types of revenue guarantees for revenue-ordered assortments: If there are k distinct revenues $r_{1},$ $r_{2},$ ., $r_{k}$ associated with the products (listed in increasing order), then revenue-ordered assortments approximate the optimum revenue to within a factor of (A) 1/k; (B) 1/(1 + $ln(r_{k}/r_{1})),$ and (C) 1/(1 + ln υ), where υ is defined with respect to an optimal assortment $S^{}$ as the ratio between the probability of just buying a product and that of buying a product with highest revenue in $S^{}.$ These three guarantees are in general incomparable, that is, (A), (B), or (C) can be the largest depending on the instance. We also show that the three bounds (A), (B), and (C) are exactly tight, in the sense that none of the bounds remains true if multiplied by a factor (1+ ε) for any ε > 0. When applied to the special case of Mixed MNL models, bound (B) improves the recent analysis of revenue-ordered assortments by Rusmevichientong et al.(POMS, 2014), who showed a bound of 1/(e(1 + $ln(r_{k}/r_{1}))).$ Our second contribution is to draw a connection between assortment optimisation and some pricing problems studied in the theoretical computer science literature by showing that these pricing problems can be restated as an assortment problem under a discrete choice model satisfying the above-mentioned rationality assumption. This includes unit demand envy-free pricing problems and the Stackelberg minimum spanning tree problem. Building on that connection, we then observe that a well-studied heuristic in that area called uniform pricing corresponds in fact to the revenue-ordered assortment strategy for the specifically constructed discrete choice models. As a consequence, our revenue guarantees for revenue-ordered assortments apply. Interestingly, the resulting bounds match and unify known results on uniform pricing that were proved separately in the literature for the envy-free pricing problems and the Stackelberg minimum spanning tree problem. This paper is available at https://arxiv.org/abs/1606.01371.
Starting Page	345
Ending Page	346
Page Count	2
File Format	PDF
ISBN	9781450345279
DOI	10.1145/3033274.3084084
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2017-06-20
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Discrete choice models Pricing Assortment optimization Revenue management Regularity
Content Type	Text
Resource Type	Article

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