Multi-Objective Assortment Optimization: Profit, Risk, Customer Utility, and Beyond

Assortment optimization is a fundamental challenge in revenue management, aiming to offer a subset from all products on hand to maximize expected revenue. However, businesses often face multiple goals that go far beyond revenue, and these goals are sometimes even in conflict with each other. In this study, we introduce a comprehensive framework and a new reformulation technique for tackling multi-objective assortment optimization problems. We focus on the sum of multiple convex objective functions (i.e., the tradeoff between distinct objectives), and we propose a reformulation that effectively “linearizes” the problem. We demonstrate that this reformulated problem is equivalent to the original and provides a unified solution approach for various multi-objective contexts. Our method covers a broad range of operational objectives, such as risk, customer utility, market share, costs with economies of scale, and dualized convex constraints. We analyze the multi-objective problem in the context of the multinomial logit model, the nested logit model, and the Markov chain choice model, and demonstrate the efficiency and practicality of our approach through extensive numerical experiments. Our work presents a powerful and versatile tool for addressing multi-objective assortment problems frequently encountered in real-world revenue management scenarios.