Quasi-polynomial time approximation schemes for assortment optimization under Mallows-based rankings

In spite of its widespread applicability in learning theory, probability, combinatorics, and in various other fields, the Mallows model has only recently been examined from revenue management perspectives. To our knowledge, the only provably-good approaches for assortment optimization under the Mall...

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Veröffentlicht in:Mathematical programming Jg. 208; H. 1-2; S. 111 - 171
Hauptverfasser: Rieger, Alon, Segev, Danny
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2024
Springer
Schlagworte:
Algorithms
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
Mallows model
Assortment optimization
90C39
Dynamic programming
68W25
90C27
Quasi-PTAS
ISSN:0025-5610, 1436-4646
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Zusammenfassung:In spite of its widespread applicability in learning theory, probability, combinatorics, and in various other fields, the Mallows model has only recently been examined from revenue management perspectives. To our knowledge, the only provably-good approaches for assortment optimization under the Mallows model have recently been proposed by Désir et al. (Oper Res 69(4):1206–1227, 2021), who devised three approximation schemes that operate in very specific circumstances. Unfortunately, these algorithmic results suffer from two major limitations, either crucially relying on strong structural assumptions, or incurring running times that exponentially scale either with the ratio between the extremal prices or with the Mallows concentration parameter. The main contribution of this paper consists in devising a quasi-polynomial-time approximation scheme for the assortment optimization problem under the Mallows model in its utmost generality. In other words, for any accuracy level ϵ > 0 , our algorithm identifies an assortment whose expected revenue is within factor 1 - ϵ of optimal, without resorting to any structural or parametric assumption whatsoever. Our work sheds light on newly-gained structural insights surrounding near-optimal Mallows-based assortments and fleshes out some of their unexpected algorithmic consequences.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-023-02033-4