Technical Note—Approximation Schemes for Capacity-Constrained Assortment Optimization Under the Nested Logit Model

Abstract

This paper proposes a carefully crafted dynamic programming approach for capacitated assortment optimization under the nested logit model in its utmost generality, potentially including partially captured nests and possibly synergistic products. Specifically, we show that the optimal revenue can be efficiently approached within any degree of accuracy through synthesizing ideas related to continuous-state dynamic programming, state space discretization, and sensitivity analysis of modified revenue functions. These developments allow us to devise the first fully polynomial-time approximation scheme in this context, thus resolving fundamental open questions posed in earlier literature.