Pricing and Assortment Optimization Under Logit‐Based Choice Models With Tree‐Structured Consideration Sets
研究了在两种树状考虑集结构下，基于对数选择模型的定价与品类优化问题，提出了统一框架来设计全多项式时间近似方案，以最大化期望收益。
ABSTRACT We study pricing and assortment optimization problems under logit‐based choice models with two tree‐structured consideration sets, that is, the subtree structure and the induced paths structure. In each model, there are multiple customer types, and each customer type is a combination of the product preference vector and the consideration set. A customer of a particular type only purchases products within his consideration set. The tree structure means all products form a tree with each node representing one product, and all consideration sets are induced from this tree. In the subtree structure, each consideration set consists of products in a subtree, and in the induced paths structure, each consideration set consists of products on the path from one node to the root. Customers make purchase decisions following the mixed multinomial logit model (MMNL) or the multilevel nested logit model (multilevel NL). The goal of the pricing and assortment optimization is to determine a set of products offered to customers along with the prices such that the expected revenue is maximized. We consider both the unconstrained problem and the capacitated problem. We propose a unified framework, which captures the tree structure, to design fully polynomial time approximation schemes (FPTAS) for all these problems.