Assortment Optimization with Replacement Options for Retail Platforms with Stockout Risk

There has been a notable surge of online platforms that operate as market facilitators without having direct control over the inventory of the products they sell. When an online platform operates as a market facilitator, the products offered to a customer may have a significant probability of being out of stock when the order placed by the customer is being fulfilled. Therefore, such online platforms often prompt the customers to pick not only a preferred option, but also a replacement option, in case their preferred option is out of stock when fulfilling the order. We study assortment optimization problems when the customers are offered assortments of products among which they pick their preferred and replacement options. If the preferred option is available, then they are provided with the preferred option. If the preferred option is not available, but the replacement option is, then they are provided with the replacement option. Otherwise, the customers are provided with no products. We use a version of the multinomial logit model to capture the choice process of the customers. We consider two variants of the problem. In the nonadaptive variant, we compute one assortment of products among which the customers pick their both preferred and replacement options. In the adaptive variant, the assortment of products among which the customer chooses her replacement option depends on the preferred option she picked. We show that both variants are NP-hard. Our main technical contributions are a polynomial-time approximation scheme for the adaptive variant and a fully polynomial-time approximation scheme for the nonadaptive variant. Using data from Instacart, we demonstrate that explicitly modeling the presence of a replacement option and using an adaptive strategy to offer assortments for the replacement option can provide significant revenue benefits.

Funding: H. Topaloglu was supported in part by NSF [Grant CMMI-2226900].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.1074.