Assortment Optimization in the Presence of Focal Effect: Operational Insights and Efficient Algorithms

This paper considers the scenario where the assortment provided by the seller can influence customers' evaluation of item utility. A possible consequence is that certain items in an assortment become ``star items" to customers, and customers over-evaluate their utilities. We call such a phenomenon the focal effect. Kovach and Tserenjigmid (2022) propose a focal Luce model (FLM) to describe customers' choices in the presence of the focal effect. FLM is a new variant of the classic Luce model (also known as the multinomial logit choice model) equipped with a ``focal machine" to describe the focal effect. The merit of FLM lies in its great flexibility to capture customers' different psychologies that lead to different choice behaviors. As a result, FLM can serve as a general framework to cover many practical scenarios. On the optimization front, we establish that the assortment optimization problem under the FLM is NP-hard in general. However, we still identify some structures of the optimal assortment that lead to operational insights of the model. We find that the assortment optimization can be solved in polynomial time by imposing assumptions on the model's ``focal machine", and these assumptions are satisfied in many practical scenarios. This polynomial-solvability is reserved even for the more complex joint assortment and pricing optimization problem. In conclusion, FLM strikes a balance between model flexibility and traceability---the great flexibility of FLM in capturing the focal effect in many scenarios does not come at a high operational tractability cost.