Constrained Assortment Optimization for the Nested Logit Model
研究了嵌套Logit模型下受品类数量或空间限制的品类优化问题，证明了数量约束下可通过线性规划高效求解，空间约束下为NP难问题并给出了2倍近似算法。
We study assortment optimization problems where customer choices are governed by the nested logit model and there are constraints on the set of products offered in each nest. Under the nested logit model, the products are organized in nests. Each product in each nest has a fixed revenue associated with it. The goal is to find a feasible set of products, i.e., a feasible assortment, to maximize the expected revenue per customer. We consider cardinality and space constraints on the offered assortment, which limit the number of products and the total space consumption of the products offered in each nest, respectively. We show that the optimal assortment under cardinality constraints can be obtained efficiently by solving a linear program. The assortment optimization problem under space constraints is NP-hard. We show how to obtain an assortment with a performance guarantee of 2 under space constraints. This assortment also provides a performance guarantee of 1/(1-ϵ) when the space requirement of each product is at most a fraction ϵ of the space availability in each nest. Building on our results for constrained assortment optimization, we show that we can efficiently solve joint assortment optimization and pricing problems under the nested logit model, where we choose the assortment of products to offer to customers, as well as the prices of the offered products. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2014.1931 . This paper was accepted by Dimitris Bertsimas, optimization.