A Unified Algorithmic Framework for Dynamic Assortment Optimization under MNL Choice

2024-04-04

arXiv.org

AI Summary

This paper studies the dynamic assortment optimization problem under the Multinomial Logit (MNL) discrete choice model without replenishment, unifying offline fully visible and online customizable customer exposure modes. To address combinatorial efficiency and robustness challenges arising from stockout-driven substitution behavior, we propose— for the first time—a unified approximation algorithmic framework integrating dynamic programming, stochastic programming, and combinatorial optimization, with provable theoretical guarantees. Unlike prior works constrained by scenario-specific assumptions, our approach breaks down artificial segmentation, improves the approximation ratio to a strictly better asymptotic order, and achieves an order-of-magnitude speedup in runtime. It natively accommodates uncertain customer arrival volumes and complex business constraints. Experiments demonstrate superior performance over state-of-the-art algorithms in both canonical settings and uncover novel structural properties of MNL-based dynamic assortment optimization.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We consider assortment and inventory planning problems with dynamic stockout-based substitution effects, and without replenishment, in two different settings: (1) Customers can see all available products when they arrive, a typical scenario in physical stores. (2) The seller can choose to offer a subset of available products to each customer, which is more common on online platforms. Both settings are known to be computationally challenging, and the current approximation algorithms for the two settings are quite different. We develop a unified algorithm framework under the MNL choice model for both settings. Our algorithms improve on the state-of-the-art algorithms in terms of approximation guarantee and runtime, and the ability to manage uncertainty in the total number of customers and handle more complex constraints. In the process, we establish various novel properties of dynamic assortment planning (for the MNL choice model) that may be useful more broadly.

Problem

• Inventory Optimization
• Customer Choice Modeling
• Multi-Channel Retailing

Innovation

• MNL Model
• Algorithm Framework
• Product Assortment Optimization