Robust Assortment Optimization under a Ranking-based Choice Model with Product Unavailability Effect

TL;DR

This paper develops a robust optimization framework for assortment planning under a ranking-based choice model that accounts for product unavailability, offering efficient algorithms for both special and general cases.

Contribution

It introduces a bi-level optimization model incorporating product unavailability effects and proposes polynomial-time and iterative algorithms for solving the problem.

Findings

Polynomial-time solution for a special case.

A cutting-plane method for the general problem.

A greedy algorithm for large instances.

Abstract

The assortment planning problem is a central piece in the revenue management strategy of any company in the retail industry. In this paper, we study a robust assortment optimization problem for substitutable products under a sequential ranking-based choice model. Our modeling approach incorporates the cumulative effect of finding multiple unavailable products on the customers' purchase decisions. To model the highly uncertain order in which a customer explores the products to buy, we present a bi-level optimization approach to maximize the expected revenue under the worst-case order of products in the preference lists of customers. We provide a polynomial-time algorithm that optimally solves a special case of the unconstrained assortment planning problem under our choice model. For the general constrained version of the problem, we devise a solution procedure that includes a single-level reformulation and a cutting-plane approach to iteratively tighten the solution space. We also provide a greedy algorithm that can quickly solve large instances with small optimality gaps.