Continuous Assortment Optimization with Logit Choice Probabilities and Incomplete Information

Yannik Peeters (), Arnoud V. den Boer () and Michel Mandjes ()
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Yannik Peeters: Amsterdam Business School, University of Amsterdam, 1018 TV Amsterdam, Netherlands
Arnoud V. den Boer: Amsterdam Business School, University of Amsterdam, 1018 TV Amsterdam, Netherlands; Korteweg-de Vries Institute for Mathematics, University of Amsterdam, 1098 XG Amsterdam, Netherlands
Michel Mandjes: Amsterdam Business School, University of Amsterdam, 1018 TV Amsterdam, Netherlands; Korteweg-de Vries Institute for Mathematics, University of Amsterdam, 1098 XG Amsterdam, Netherlands

Operations Research, 2022, vol. 70, issue 3, 1613-1628

Abstract: We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller’s problem consists of determining the optimal subset of products to offer to potential customers. To describe the relation between assortment and customer choice, we propose a probabilistic choice model that forms the continuous counterpart of the widely studied discrete multinomial logit model. We consider the seller’s problem under incomplete information, propose a stochastic-approximation type of policy, and show that its regret, its performance loss compared with the optimal policy, is only logarithmic in the time horizon. We complement this result by showing a matching lower bound on the regret of any policy, implying that our policy is asymptotically optimal. We then show that adding a capacity constraint significantly changes the structure of the problem: we construct a policy and show that its regret after T time periods is bounded above by a constant times T 2 / 3 (up to a logarithmic term); in addition, we show that the regret of any policy is bounded from below by a positive constant times T 2 / 3 , so that also in the capacitated case, we obtain asymptotic optimality. Numerical illustrations show that our policies outperform or are on par with alternatives.

Keywords: Marketing Analytics and Revenue Management; assortment optimization; learning; multiarmed bandit; continuous assortment (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:70:y:2022:i:3:p:1613-1628

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