An extended ε$\varepsilon $‐constraint method for a bi‐objective assortment optimization problem

Abstract

The paper deals with assortment optimization when customers purchase products using a nonparametric choice model. Each customer is presented with a preference list and will buy an available highest‐ranked offered product on the preference list. The paper presents a novel bi‐objective integer programming model for assortment optimization following a ranking‐based consumer choice model. The objectives are maximizing the expected revenue and maximizing customer satisfaction. This problem is recognized as an NP‐hard problem. After developing the bi‐objective model, an improved version of the augmented ε‐constraint method is proposed to solve the problem and retrieve the Pareto‐optimal solutions. In each iteration, this algorithm solves a single‐objective linear integer programming sub‐problem. Our approach aims to obtain a complete set of Pareto‐optimal solutions. Finally, we present computational experiments on synthetic data. Several numerical illustrations are provided at the end to demonstrate the application of the proposed methodology. The computational results provide the decision‐makers with valuable information regarding the factors that mainly affect the solutions.