Defines exact adaptivity gaps of e/(e-1) and 2 between policy classes for two-sided assortment optimization and provides 1/4-approximation for adaptive one-by-one policies plus 0.067-approximation for simultaneous policies under MNL, with extensions to constrained settings.
(31) Given the above, let (Modified Primal) be Problem (25) with the following modified constraints: X C⊆C λj,C = e e − 1 , for all j ∈ S, (32) X S⊆S τi,S = e e − 1 , for all i ∈ C
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Two-sided Assortment Optimization: Adaptivity Gaps and Approximation Algorithms
Defines exact adaptivity gaps of e/(e-1) and 2 between policy classes for two-sided assortment optimization and provides 1/4-approximation for adaptive one-by-one policies plus 0.067-approximation for simultaneous policies under MNL, with extensions to constrained settings.